\section{Introduction}

These notes are organized as follows:

\begin{itemize}
\item in Section \ref{sec1}, we give some details in the computations involved in the last section of \cite[\S 6]{jeju3};
\item in Section \ref{sec2}, we give some details in the computations involved in the proof of \cite[Theorem 5.1]{jeju4} for the affine Weyl group of type $\tilde{G}_{2}$. We also give the left order on the left cells for all choices of parameters.
\item in Section \ref{sec3}, we describe the partition of  the affine Weyl group of type $\tilde{B}_{2}$ into cells for all parameters.
\item in Section \ref{sec4}, we give some details in the computations involved in the proof of \cite[Theorem 5.3]{jeju4} for the affine Weyl group of type $\tilde{B}_{2}$. We also give the left order on the left cells for all choices of parameters.

\end{itemize}

\section{Computations in \cite[\S 6]{jeju3}}
\label{sec1}
Let $W$ be the affine Weyl group of type $\tilde{G_{2}}$ with diagram and weight function given by
\begin{center}
\begin{picture}(150,32)
\put(  0, 10){$\tilde{G}_2$}
\put( 40, 10){\circle{10}}
\put( 44,  7){\line(1,0){33}}
\put( 45,  10){\line(1,0){30.5}}
\put( 44, 13){\line(1,0){33}}
\put( 81, 10){\circle{10}}
\put( 86, 10){\line(1,0){29}}
\put(120, 10){\circle{10}}
\put( 38, 20){$a$}
\put( 78, 20){$b$}
\put(118, 20){$b$}
\put( 38, -3){$s_{1}$}
\put( 78, -3){$s_{2}$}
\put(118,-3){$s_{3}$}
\end{picture}
\end{center}
where $a,b$ are positive integers such that $a/b>4$. In this section we go through the proof of Lemma 6.4, Claim 6.6 and Claim 6.8 in \cite{jeju3} and give some details in the computations involved. \\
$\ $\\

We keep the notation of \cite[\S 6]{jeju3}. Recall that
$\ $\\
\begin{center}
\begin{pspicture}(-6.2,-8.2)(6.2,6.9)
\psset{unit=1cm}
\SpecialCoor
\psline(0,-6)(0,6)
\multido{\n=1+1}{7}{
\psline(\n;30)(\n;330)}
\rput(1;30){\psline(0,0)(0,5.5)}
\rput(1;330){\psline(0,0)(0,-5.5)}
\rput(2;30){\psline(0,0)(0,5)}
\rput(2;330){\psline(0,0)(0,-5)}
\rput(3;30){\psline(0,0)(0,4.5)}
\rput(3;330){\psline(0,0)(0,-4.5)}
\rput(4;30){\psline(0,0)(0,4)}
\rput(4;330){\psline(0,0)(0,-4)}
\rput(5;30){\psline(0,0)(0,3.5)}
\rput(5;330){\psline(0,0)(0,-3.5)}
\rput(6;30){\psline(0,0)(0,3)}
\rput(6;330){\psline(0,0)(0,-3)}
\rput(7;30){\psline(0,0)(0,2.5)}
\rput(7;330){\psline(0,0)(0,-2.5)}
\multido{\n=1+1}{7}{
\psline(\n;150)(\n;210)}
\rput(1;150){\psline(0,0)(0,5.5)}
\rput(1;210){\psline(0,0)(0,-5.5)}
\rput(2;150){\psline(0,0)(0,5)}
\rput(2;210){\psline(0,0)(0,-5)}
\rput(3;150){\psline(0,0)(0,4.5)}
\rput(3;210){\psline(0,0)(0,-4.5)}
\rput(4;150){\psline(0,0)(0,4)}
\rput(4;210){\psline(0,0)(0,-4)}
\rput(5;150){\psline(0,0)(0,3.5)}
\rput(5;210){\psline(0,0)(0,-3.5)}
\rput(6;150){\psline(0,0)(0,3)}
\rput(6;210){\psline(0,0)(0,-3)}
\rput(7;150){\psline(0,0)(0,2.5)}
\rput(7;210){\psline(0,0)(0,-2.5)}
\multido{\n=1.5+1.5}{4}{
\psline(-6.062,\n)(6.062,\n)}
\multido{\n=0+1.5}{5}{
\psline(-6.062,-\n)(6.062,-\n)}
\psline(0;0)(7;30)

\rput(0,1){\psline(0;0)(7;30)}
\rput(0,1){\psline(0;0)(7;210)}
\rput(0,2){\psline(0;0)(7;30)}
\rput(0,2){\psline(0;0)(7;210)}
\rput(0,3){\psline(0;0)(6;30)}
\rput(0,3){\psline(0;0)(7;210)}
\rput(0,4){\psline(0;0)(4;30)}
\rput(0,4){\psline(0;0)(7;210)}
\rput(0,5){\psline(0;0)(2;30)}
\rput(0,5){\psline(0;0)(7;210)}
\rput(0,6){\psline(0;0)(7;210)}
\rput(-1.732,6){\psline(0;0)(5;210)}
\rput(-3.464,6){\psline(0;0)(3;210)}
\rput(-5.196,6){\psline(0;0)(1;210)}

\rput(0,-1){\psline(0;0)(7;30)}
\rput(0,-1){\psline(0;0)(7;210)}
\rput(0,-2){\psline(0;0)(7;30)}
\rput(0,-2){\psline(0;0)(7;210)}
\rput(0,-3){\psline(0;0)(7;30)}
\rput(0,-3){\psline(0;0)(6;210)}
\rput(0,-4){\psline(0;0)(7;30)}
\rput(0,-4){\psline(0;0)(4;210)}
\rput(0,-5){\psline(0;0)(7;30)}
\rput(0,-5){\psline(0;0)(2;210)}
\rput(0,-6){\psline(0;0)(7;30)}
\rput(1.732,-6){\psline(0;0)(5;30)}
\rput(3.464,-6){\psline(0;0)(3;30)}
\rput(5.196,-6){\psline(0;0)(1;30)}

\psline(0;0)(6.928;60)
\rput(1.732,0){\psline(0;0)(6.928;60)}
\rput(3.464,0){\psline(0;0)(5.196;60)}
\rput(5.196,0){\psline(0;0)(1.732;60)}
\rput(1.732,0){\psline(0;0)(6.928;240)}
\rput(3.464,0){\psline(0;0)(6.928;240)}
\rput(5.196,0){\psline(0;0)(6.928;240)}
\rput(6.062,-1.5){\psline(0;0)(5.196;240)}
\rput(6.062,-4.5){\psline(0;0)(1.732;240)}
\rput(-1.732,0){\psline(0;0)(6.928;60)}
\rput(-3.464,0){\psline(0;0)(6.928;60)}
\rput(-5.196,0){\psline(0;0)(6.928;60)}
\rput(-1.732,0){\psline(0;0)(6.928;240)}
\rput(-3.464,0){\psline(0;0)(5.196;240)}
\rput(-5.196,0){\psline(0;0)(1.732;240)}
\rput(-6.062,1.5){\psline(0;0)(5.196;60)}
\rput(-6.062,4.5){\psline(0;0)(1.732;60)}

\psline(0;0)(6.928;120)
\psline(0;0)(6.928;300)
\rput(-1.732,0){\psline(0;0)(6.928;120)}
\rput(-3.464,0){\psline(0;0)(5.196;120)}
\rput(-5.196,0){\psline(0;0)(1.732;120)}
\rput(-1.732,0){\psline(0;0)(6.928;300)}
\rput(-3.464,0){\psline(0;0)(6.928;300)}
\rput(-5.196,0){\psline(0;0)(6.928;300)}
\rput(-6.062,-1.5){\psline(0;0)(5.196;300)}
\rput(-6.062,-4.5){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;300)}
\rput(3.464,0){\psline(0;0)(5.196;300)}
\rput(5.196,0){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;120)}
\rput(3.464,0){\psline(0;0)(6.928;120)}
\rput(5.196,0){\psline(0;0)(6.928;120)}
\rput(6.062,1.5){\psline(0;0)(5.196;120)}
\rput(6.062,4.5){\psline(0;0)(1.732;120)}

\rput(0,1){\psline(0;0)(7;150)}
\rput(0,1){\psline(0;0)(7;330)}
\rput(0,2){\psline(0;0)(7;150)}
\rput(0,2){\psline(0;0)(7;330)}
\rput(0,3){\psline(0;0)(6;150)}
\rput(0,3){\psline(0;0)(7;330)}
\rput(0,4){\psline(0;0)(4;150)}
\rput(0,4){\psline(0;0)(7;330)}
\rput(0,5){\psline(0;0)(7;330)}
\rput(0,6){\psline(0;0)(7;330)}
\rput(-1.732,6){\psline(0;0)(2;330)}

\rput(0,-1){\psline(0;0)(7;150)}
\rput(0,-1){\psline(0;0)(7;330)}
\rput(0,-2){\psline(0;0)(7;150)}
\rput(0,-2){\psline(0;0)(7;330)}
\rput(0,-3){\psline(0;0)(7;150)}
\rput(0,-3){\psline(0;0)(6;330)}
\rput(0,-4){\psline(0;0)(7;150)}
\rput(0,-4){\psline(0;0)(4;330)}
\rput(0,-5){\psline(0;0)(7;150)}
\rput(0,-5){\psline(0;0)(2;330)}
\rput(0,-6){\psline(0;0)(7;150)}

\rput(6.062,3.5){\psline(0;0)(5;150)}
\rput(6.062,4.5){\psline(0;0)(3;150)}
\rput(6.062,5.5){\psline(0;0)(1;150)}

\rput(-6.062,-3.5){\psline(0;0)(5;330)}
\rput(-6.062,-4.5){\psline(0;0)(3;330)}
\rput(-6.062,-5.5){\psline(0;0)(1;330)}

\psline(0;0)(7;330)
\psline(0;0)(7;150)
\psline(0;0)(7;210)
\psline(0;0)(6.928;240)

\pspolygon[linewidth=0.7mm](0,0)(0,1)(0.433,0.75)
\pspolygon[linewidth=0.7mm](0,0)(0,1)(-0.866,1.5)
\pspolygon[linewidth=0.7mm](0,0)(-0.433,0.75)(-1.732,0)(-0.866,0)(-0.866,-1.5)
\pspolygon[linewidth=0.7mm](0,0)(0.433,0.75)(1.732,0)(0.866,0)(0.866,-1.5)
\pspolygon[linewidth=0.7mm](0,1)(0,1.5)(-0.866,1.5)
\pspolygon[linewidth=0.7mm](0,1)(0,3)(0.433,2.25)(1.732,3)(0.433,0.75)
\psline[linewidth=0.7mm](0,0)(0,-6)
\psline[linewidth=0.7mm](0;0)(6.928;240)
\rput(0.866,-1.5){\psline[linewidth=0.7mm](0;0)(4.5;270)}
\rput(0.866,-1.5){\psline[linewidth=0.7mm](0;0)(5.196;300)}
\rput(1.732,0){\psline[linewidth=0.7mm](0;0)(6.928;300)}
\rput(2.598,-1.5){\psline[linewidth=0.7mm](0;0)(4;330)}
\rput(1.732,0){\psline[linewidth=0.7mm](0;0)(5;330)}
\rput(1.732,0){\psline[linewidth=0.7mm](0;0)(4.33;0)}
\rput(0.866,1.5){\psline[linewidth=0.7mm](0;0)(5.196;0)}
\rput(0.866,1.5){\psline[linewidth=0.7mm](0;0)(6;30)}
\rput(2.598,1.5){\psline[linewidth=0.7mm](0;0)(4;30)}
\rput(1.732,3){\psline[linewidth=0.7mm](0;0)(3.464;60)}
\rput(0,3){\psline[linewidth=0.7mm](0;0)(3.464;60)}
\rput(0.866,4.5){\psline[linewidth=0.7mm](0;0)(1.5;90)}
\rput(0,3){\psline[linewidth=0.7mm](0;0)(3;90)}
\rput(0,3){\psline[linewidth=0.7mm](0;0)(3.464;120)}
\rput(-0.866,1.5){\psline[linewidth=0.7mm](0;0)(5.196;120)}
\rput(-0.866,1.5){\psline[linewidth=0.7mm](0;0)(6;150)}
\rput(-0.866,1.5){\psline[linewidth=0.7mm](0;0)(5.196;180)}
\rput(-2.598,1.5){\psline[linewidth=0.7mm](0;0)(4;150)}
\rput(-1.732,0){\psline[linewidth=0.7mm](0;0)(4.33;180)}
\rput(-1.732,0){\psline[linewidth=0.7mm](0;0)(5;210)}
\rput(-1.732,0){\psline[linewidth=0.7mm](0;0)(6.928;240)}
\rput(-1.732,0){\psline[linewidth=0.7mm](0;0)(6.928;240)}
\rput(-2.598,-1.5){\psline[linewidth=0.7mm](0;0)(4;210)}
\rput(0,1.5){\psline[linewidth=0.7mm](0;1.5)(0.866;1.5)}

\rput(0.17,0.68){{\tiny $A_{0}$}}
\rput(-1.5,-4.33){{\small $A_{1}$}}
\rput(-4.97,-4.3){{\small $A'_{6}$}}
\rput(-4.97,-1.3){{\small $A_{6}$}}
\rput(-4.97,1.7){{\small $A'_{5}$}}
\rput(-2.372,3.2){{\small $A_{5}$}}
\rput(-0.23,4.67){{\small $A_{4}$}}
\rput(1.1,5.85){{\small $A'_{4}$}}
\rput(2.824,3.2){{\small $A_{3}$}}
\rput(3.69,1.7){{\small $A'_{3}$}}
\rput(5.452,-1.31){{\small $A_{2}$}}
\rput(5.452,-4.31){{\small $A'_{2}$}}
\rput(1.988,-4.31){{\small $A'_{1}$}}
\psline[linewidth=0.5mm]{->}(0.433,5.75)(0.433,6.75)
\rput(0.433,7){$C_{4}$}
\rput(5.812,3.8){\psline[linewidth=0.5mm]{->}(0;0)(1;30)}
\rput(7,4.4){$C_{3}$}
\rput(5.812,-2.8){\psline[linewidth=0.5mm]{->}(0;0)(1;330)}
\rput(7,-3.4){$C_{2}$}
\psline[linewidth=0.5mm]{->}(0.433,-5.75)(0.433,-6.75)
\rput(0.433,-7){$C_{1}$}
\rput(-5.812,-2.8){\psline[linewidth=0.5mm]{->}(0;0)(1;210)}
\rput(-7,-3.4){$C_{6}$}
\rput(-5.812,3.8){\psline[linewidth=0.5mm]{->}(0;0)(1;150)}
\rput(-7,4.4){$C_{5}$}
\rput(2.4,5.75){\psline[linewidth=0.5mm]{->}(0;0)(1;60)}
\rput(3.05,6.83){$B_{3}$}
\rput(5.812,0.75){\psline[linewidth=0.5mm]{->}(0;0)(1;0)}
\rput(7.1,0.75){$B_{2}$}
\rput(4.132,-5.75){\psline[linewidth=0.5mm]{->}(0;0)(1;300)}
\rput(4.837,-6.83){$B_{1}$}
\rput(-4.132,-5.75){\psline[linewidth=0.5mm]{->}(0;0)(1;240)}
\rput(-4.837,-6.83){$B_{6}$}
\rput(-5.812,0.75){\psline[linewidth=0.5mm]{->}(0;0)(1;180)}
\rput(-7.1,0.75){$B_{5}$}
\rput(-2.4,5.75){\psline[linewidth=0.5mm]{->}(0;0)(1;120)}
\rput(-3.05,6.83){$B_{4}$}

\rput(0.22,1.33){\tiny $E_{1}$}

\rput(-0.32,1.01){\tiny $E_{2}$}

\rput(0.33,1.98){\tiny $D_{3}$}

\rput(-0.65,0.19){\tiny $D_{2}$}

\rput(0.65,0.17){\tiny $D_{1}$}

\rput(-.25,1.35){\tiny $F$}

\rput(0,-7.8){Figure 1. Decomposition of $\tilde{G}_{2}$ into left cells in the case $a>4b$}

\end{pspicture}
\end{center}

\subsection{The sets $C_{i}$} $\ $\\

For $1\leq i\leq 6$, let
\begin{enumerate}
\item $u_{i}\in C_{i}$ be the element of minimal length in $C_{i}$;
\item $v_{i}\in A_{i}$ be the element of minimal length in $A_{i}$;
\item $v'_{i}\in A'_{i}$ be the element of minimal length in $A'_{i}$.
\end{enumerate}
We set $U:=\{u_{i},v_{i},v'_{i}\ |\ 1\leq i\leq 6\}$, $X_{v_{i}}=X_{v'_{i}}=X_{\{s_{1},s_{2}\}}$ and
$$X_{u_{i}}=\{z\in W\ |\ zu_{i}\in C_{i}\}.$$
In this section we prove the following.
\begin{enumerate}
\item The submodule
$$\mathcal{M}:=\mathcal{h} T_{x}C_{u}\ |\ u\in U, x\in X_{u}\mathbf{i}_{\mathcal{A}}\subseteq \mathcal{H}$$
is a left ideal.
\item Let $u\in U$, $u'<u$ and $x\in X_{u}$. We have
$$P_{u',u}T_{x}C_{u}\equiv T_{xu} \mod \mathcal{H}_{<0}$$
\end{enumerate}

\noindent First we prove (1). To this end we only need to show that $T_{s_{2}}C_{u_{i}}$ and $T_{s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{i}}$ lie in $\mathcal{M}$ for all $1\leq i\leq 6$. We have
$$T_{s_{2}}C_{u_{i}}=C_{v_{i}}-v^{-b}C_{u_{i}}\quad\text{for $i=1,2,3,6$}$$
and
$$T_{s_{2}}C_{u_{4}}=C_{v_{4}}-v^{-b}C_{u_{4}}+C_{v_{2}}$$
$$T_{s_{2}}C_{u_{5}}=C_{v_{5}}-v^{-b}C_{u_{5}}+C_{v_{1}}.$$
Thus $T_{s_{2}}C_{u_{i}}\in\mathcal{M}$.\\
For $i=1,2,3,6$ we have
\begin{eqnarray*}
T_{3}C_{u_{i}}&=&C_{3u_{i}}+\mathcal{A} C_{u_{i}}\\
T_{23}C_{u_{i}}&=&C_{23u_{i}}+\mathcal{A} C_{3u_{i}}+\mathcal{A} C_{u_{i}}+\mathcal{A} C_{v_{i}}\\
T_{123}C_{u_{i}}&=&C_{123u_{i}}+\mathcal{A} C_{23u_{i}}+\mathcal{A} C_{3u_{i}}+\mathcal{A} C_{u_{i}}+\mathcal{A} C_{v_{i}}\\
T_{2123}C_{u_{i}}&=&C_{2123u_{i}}+\mathcal{A} C_{123u_{i}}+\mathcal{A} C_{3u_{i}}+\mathcal{A} C_{u_{i}}\\
T_{12123}C_{u_{i}}&=&C_{12123u_{i}}+\mathcal{A} C_{2123u_{i}}+\mathcal{A} C_{123u_{i}}+\mathcal{A} C_{u_{i}}\\
T_{212123}C_{u_{i}}&=&C_{v'_{i}}+\mathcal{A} C_{12123u_{i}}+\mathcal{A} C_{123u_{i}}+\mathcal{A} C_{u_{i}}+\mathcal{A} C_{v_{i}}\\
\end{eqnarray*}
thus
$$C_{3u_{i}},C_{23u_{i}},C_{123u_{i}},C_{2123u_{i}},C_{12123u_{i}}\in\mathcal{M}.$$
Since $C_{v'_{i}},C_{u_{i}}, C_{v_{i}}\in\mathcal{M}$ we see that $T_{212123}C_{u_{i}}\in\mathcal{M}$ as required.\\
We have
\begin{eqnarray*}
T_{3}C_{u_{4}}&=&C_{3u_{4}}+\mathcal{A} C_{u_{4}}\\
T_{23}C_{u_{4}}&=&C_{23u_{4}}+\mathcal{A} C_{3u_{4}}+\mathcal{A} C_{u_{4}}+\mathcal{A} C_{v_{4}}+\mathcal{A} C_{v_{2}}\\
T_{123}C_{u_{4}}&=&C_{123u_{4}}+\mathcal{A} C_{23u_{4}}+\mathcal{A} C_{3u_{4}}+\mathcal{A} C_{u_{4}}+\mathcal{A} C_{v_{4}}+\mathcal{A} C_{v_{2}}\\
T_{2123}C_{u_{4}}&=&C_{2123u_{4}}+\mathcal{A} C_{123u_{4}}+\mathcal{A} C_{3u_{4}}+\mathcal{A} C_{u_{4}}\\
T_{12123}C_{u_{4}}&=&C_{12123u_{4}}+\mathcal{A} C_{2123u_{4}}+\mathcal{A} C_{123u_{4}}+\mathcal{A} C_{u_{4}}\\
T_{212123}C_{u_{4}}&=&C_{v'_{i}}+\mathcal{A} C_{12123u_{4}}+\mathcal{A} C_{123u_{4}}+\mathcal{A} C_{u_{4}}+\mathcal{A} C_{v_{4}}+\mathcal{A} C_{v_{2}}\\
\end{eqnarray*}
thus
$$C_{3u_{i}},C_{23u_{i}},C_{123u_{i}},C_{2123u_{i}},C_{12123u_{i}}\in\mathcal{M}.$$
Since $C_{v'_{i}},C_{u_{i}}, C_{v_{i}}\in\mathcal{M}$ we see that $T_{212123}C_{u_{4}}\in\mathcal{M}$ as required.\\
We have
\begin{eqnarray*}
T_{3}C_{u_{5}}&=&C_{3u_{5}}+\mathcal{A} C_{u_{5}}\\
T_{23}C_{u_{5}}&=&C_{23u_{5}}+\mathcal{A} C_{3u_{5}}+\mathcal{A} C_{u_{5}}+\mathcal{A} C_{v_{5}}+\mathcal{A} C_{v_{1}}\\
T_{123}C_{u_{5}}&=&C_{123u_{5}}+\mathcal{A} C_{23u_{5}}+\mathcal{A} C_{3u_{5}}+\mathcal{A} C_{u_{5}}+\mathcal{A} C_{v_{5}}+\mathcal{A} C_{v_{1}}\\
T_{2123}C_{u_{5}}&=&C_{2123u_{5}}+\mathcal{A} C_{123u_{5}}+\mathcal{A} C_{3u_{5}}+\mathcal{A} C_{u_{5}}\\
T_{12123}C_{u_{5}}&=&C_{12123u_{5}}+\mathcal{A} C_{2123u_{5}}+\mathcal{A} C_{123u_{5}}+\mathcal{A} C_{u_{5}}\\
T_{212123}C_{u_{5}}&=&C_{v'_{i}}+\mathcal{A} C_{12123u_{5}}+\mathcal{A} C_{123u_{5}}+\mathcal{A} C_{u_{5}}+\mathcal{A} C_{v_{5}}+\mathcal{A} C_{v_{1}}\\
\end{eqnarray*}
thus
$$C_{3u_{i}},C_{23u_{i}},C_{123u_{i}},C_{2123u_{i}},C_{12123u_{i}}\in\mathcal{M}.$$
Since $C_{v'_{i}},C_{u_{i}}, C_{v_{i}}\in\mathcal{M}$ we see that $T_{212123}C_{u_{5}}\in\mathcal{M}$ as required.\\
Statement (1) follows.

\vspace{.5cm}
\noindent
Before proving (2), we need to introduce some definitions. For $w\in W$ we set
$$Y(w)=\{y\in W | \ell(wy^{-1})=\ell(w)-\ell(y)\}.$$
We have $y\in Y(w)$ if and only if there exists a reduced expression $s_{1}\ldots s_{n}$ of $w$ and $1\leq i\leq n$ such that $y=s_{i}\ldots s_{n}$. Recall the definition of translation in \cite[Definition 4.1]{jeju1}.
\begin{Cl}
\label{trans}
Let $w\in W$ be a translation. Let $z\in W$. The following statements are equivalent
\begin{enumerate}
\item $\ell(wz)=\ell(w)+\ell(z)$;
\item $\ell(xz)=\ell(x)+\ell(z) \text{ for all $x\in \{zw^{n}| z\in Y(w), n\in\mathbb{N} \}$}$.
\end{enumerate}
\end{Cl}
\begin{proof}
The fact that (2) implies (1) is clear since $w\in \{zw^{n}| z\in Y(w), n\in\mathbb{N} \}$. Assume that (1) holds. Then using \cite[Lemma 4.2]{jeju1} in its right version we get
$$\ell(wz)=\ell(w)+\ell(z)\Leftrightarrow \ell(w^{n}z)=\ell(w^{n})+\ell(z).$$
Let $x\in  \{zw^{n}| z\in Y(w), n\in\mathbb{N} \}$. Let $y\in Y_{w}$ and $n\in \mathbb{N}$ be such that $x=yw^{n}$. We have
$$\ell(wz)=\ell(w)+\ell(z)\Rightarrow \ell(w^{n+1}z)=\ell(w^{n+1})+\ell(z)\Rightarrow \ell(yw^{n}z)=\ell(yw^{n})+\ell(z)$$
as required.
\end{proof}

\vspace{.5cm}
We now prove (2).  Let $w=s_{1}s_{2}s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3}$. Note that $w$ is a translation. We have
$$X_{u_{i}}=\{yw^{n}| y\in Y(w), n\in\mathbb{N}\}.$$
Let $u<u_{i}$. Using GAP one can show that for all $y\in Y(w)$ we have
$$P_{u,u_{i}}T_{y}C_{u}\equiv T_{yu} \mod \mathcal{H}_{<0}.$$
Next, one can show that
$$P_{u,u_{i}}T_{w}C_{u}=T_{wu}+\sum_{z\in W} a_{z}T_{z}$$
where $a_{z}\in \mathcal{A}_{<0}$ and if $a_{z}\neq 0$ then $z$ satisfy $\ell(wz)=\ell(w)+\ell(z)$. Now let $x=yw^{n}\in X_{u_{i}}$ (where $y\in Y(w)$ and $n\in\mathbb{N}^{*}$). Then using Claim \ref{trans} we obtain
$$\begin{array}{ccl}
P_{u,u_{i}}T_{x}C_{u}&=&T_{yw^{n-1}}\bigg(T_{wu}+\sum_{z\in W} a_{z}T_{z}\bigg)\\
&=& T_{xu}+\underset{z\in W}{\sum}  a_{z}T_{yw^{n-1}z}\\
&\equiv& T_{xu} \mod \mathcal{H}_{<0}
\end{array}$$
and statement (2) follows.
$\ $\\

\subsection{Proof of Claim 6.6} $\ $\\

\noindent Let $u=s_{1}s_{3}s_{2}s_{1}$ and recall that
\begin{align*}
u_{1}&=s_{1}s_{2}s_{1}s_{2}s_{1},\\
v_{1}&=s_{1}s_{2}s_{1}s_{2}s_{1}s_{2},\\
v'_{1}&=s_{1}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}s_{2}s_{1}s_{2}s_{1},\\
u_{2}&=s_{1}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1},\\
v_{2}&=s_{2}s_{1}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1},\\
v'_{2}&=s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1}\\
v_{3}&=s_{2}s_{1}s_{2}s_{1}s_{2}s_{1}s_{3},
\end{align*}
and
\begin{align*}
X_{u}&:=\{z\in W| zu\in B_{1}\}\\
X_{u_{i}}&=\{z\in W\ |\ zu_{i}\in C_{i}\},\\
X_{v_{i}}&=X_{v'_{i}}=X_{\{s_{1},s_{2}\}}\quad\text{for $1\leq i\leq 6$}.
\end{align*}
Let $U:=\{u,u_{1},v_{1},v'_{1},u_{2},v_{2},v'_{2},v_{3}\}$. In this section we prove the following.
\begin{enumerate}
\item The submodule
$$\mathcal{M}:=\mathcal{h} T_{x}C_{v}\ |\ v\in U, x\in X_{u}\mathbf{i}_{\mathcal{A}}\subseteq \mathcal{H}$$
is a left ideal.
\item Let $u'<u$ and $x\in X_{u}$. We have
$$P_{u',u}T_{x}C_{u}\equiv T_{xu} \mod \mathcal{H}_{<0}$$
\end{enumerate}

\vspace{.5cm}
\noindent We prove (1). To this end it is enough to show that $T_{1212}C_{u}\in\mathcal{M}$ and $T_{1212132}C_{u}$ lie in $\mathcal{M}$. We have
\begin{eqnarray*}
T_{2}C_{u}&=&C_{2u}+\mathcal{A} C_{u}\\
T_{12}C_{u}&=&C_{12u}+ \mathcal{A} C_{2u}+\mathcal{A} C_{u}\\
T_{212}C_{u}&=&C_{212u}+\mathcal{A} C_{12u}+\mathcal{A} C_{u}\\
T_{1212}C_{u}&=&C_{u_{2}}+ \mathcal{A} C_{212u}+\mathcal{A} C_{12u}+\mathcal{A} C_{u_{1}}+\mathcal{A} C_{v_{1}}
\end{eqnarray*}
Thus $T_{1212}C_{u}\in \mathcal{M}$. \\
\newpage
We have
\begin{eqnarray*}
T_{2}C_{u}&=&C_{2u}+\mathcal{A} C_{u}\\
T_{32}C_{u}&=&C_{32u}+\mathcal{A} C_{2u}\\
T_{132}C_{u}&=&C_{132u}+ \mathcal{A} C_{32u}+\mathcal{A} C_{12u}+\mathcal{A} C_{2u}+ \mathcal{A} C_{u}\\
T_{2132}C_{u}&=&C_{2132u}+ \mathcal{A} C_{212u}+\mathcal{A} C_{132u}+\mathcal{A} C_{32u}+\mathcal{A} C_{12u}+\mathcal{A} C_{2u}+ \mathcal{A} C_{u}\\
T_{12132}C_{u}&=&C_{12132u}+ \mathcal{A} C_{2132u}+\mathcal{A} C_{212u}+\mathcal{A} C_{32u}+\mathcal{A} C_{12u}+\mathcal{A} C_{2u}\\
&&+ \mathcal{A} C_{u}+\mathcal{A} C_{u_{1}}+\mathcal{A} C_{v_{1}}+\mathcal{A} C_{u_{2}}\\
T_{212132}C_{u}&=&C_{212132u}+\mathcal{A} C_{12132u}+ \mathcal{A} C_{2132u}+\mathcal{A} C_{212u}+\mathcal{A} C_{32u}\\ &&+\mathcal{A} C_{12u}+\mathcal{A} C_{2u}+ \mathcal{A} C_{u}+\mathcal{A} C_{u_{1}}+\mathcal{A} C_{v_{2}}+\mathcal{A} C_{u_{2}}\\
T_{1212132}C_{u}&=&C_{v'_{1}}+\mathcal{A} C_{212132u}+\mathcal{A} C_{2132u} +\mathcal{A} C_{212u}+\mathcal{A} C_{32u}+\mathcal{A} C_{2u}\\
&& +\mathcal{A} C_{v_{1}}+\mathcal{A} C_{v_{2}}+\mathcal{A} C_{v_{3}}
\end{eqnarray*}
Thus $T_{1212132}C_{u}\in\mathcal{M}$ as desired.

\vspace{1cm}

\noindent We prove (2). Let $w_{1}=s_{1}s_{2}s_{3}s_{2}s_{1}s_{2}$ and $w_{2}=s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}$. These are both translations. Any $x\in X_{u}$ can be written under the form $yw_{1}^{n}$ with $y\in Y(w_{1})$ or $yw_{2}^{n}s_{3}s_{2}$ with $y\in Y(w_{2})$. One can show that for all $y_{1}\in Y(w_{1})$ and all $y_{2}\in Y(w_{2})$ we have
$$P_{u,u_{i}}T_{y_{1}}C_{u}\equiv T_{y_{1}u} \mod \mathcal{H}_{<0}\text{ and }  P_{u,u_{i}}T_{y_{2}s_{3}s_{2}}C_{u}\equiv T_{y_{2}s_{3}s_{2}u} \mod \mathcal{H}_{<0}$$
Furthermore, we have
$$P_{u,u_{i}}T_{w_{1}}C_{u}=T_{w_{1}u}+\sum_{z\in W} a_{z}T_{z}$$
where $a_{z}\in\mathcal{A}_{<0}$ and if $a_{z}\neq 0$ then $z$ satisfy $\ell(w_{1}z)=\ell(w_{1})+\ell(z)$. We have
$$P_{u,u_{i}}T_{w_{2}s_{3}s_{2}}C_{u}=T_{w_{2}s_{3}s_{2}u}+\sum_{z\in W} a'_{z}T_{z}$$
where $a'_{z}\in\mathcal{A}_{<0}$ and if $a'_{z}\neq 0$ then $z$ satisfy $\ell(w_{2}z)=\ell(w_{2})+\ell(z)$.
Arguing as in the previous section we obtain that (2) holds.\\

\subsection{Proof of Claim 6.8} $\ $\\

\noindent Recall that $v=s_{1}s_{3}s_{2}s_{1}s_{2}s_{3}$ and
$$X_{v}:=\{z\in W|zv\in B_{3}\}\qquad Y_{v}:=\{x\in X_{v}| \ell(xs_{2}s_{1}s_{2})=\ell(x)-3\}.$$
Let $U=\{v,u_{4},v_{4},v'_{4},v_{3},v_{2},v_{5}\}$.  In this section we prove the following.
\begin{enumerate}
\item The submodule
$$\mathcal{M}:=\mathcal{h} T_{x}C_{u}\ |\ u\in U, x\in X_{u}\mathbf{i}_{\mathcal{A}}\subseteq \mathcal{H}$$
is a left ideal.
\item Let $x\in X_{v}-Y_{v}$. Then we have
$$T_{x}C_{v}\equiv T_{xv} \mod \mathcal{H}_{<0}$$
\item Let $y\in Y_{v}$ and $y_{0}=s_{2}s_{1}s_{2}$. We have
$$\tilde{C}_{yv}\equiv T_{yv}+T_{y_{0}v_{3}} \mod \mathcal{H}_{<0}$$

\end{enumerate}

\vspace{.5cm}

\noindent We prove (1). To this end it is enough to show that $T_{1212}C_{u}\in\mathcal{M}$ and $T_{1212132}C_{u}$ lie in $\mathcal{M}$. We have
\begin{eqnarray*}
T_{2}C_{v}&=&C_{2v}+\mathcal{A} C_{v}\\
T_{12}C_{v}&=&C_{12v}+ \mathcal{A} C_{2v}+\mathcal{A} C_{v}\\
T_{212}C_{v}&=&C_{212v}+\mathcal{A} C_{12v}+ \mathcal{A} C_{v}+\mathcal{A} C_{v_{3}}\\
T_{1212}C_{v}&=&C_{u_{4}}+ \mathcal{A} C_{212v}+\mathcal{A} C_{12v}+\mathcal{A} C_{v_{3}}
\end{eqnarray*}
Thus $T_{1212}C_{v}\in \mathcal{M}$. We have
\begin{eqnarray*}
T_{2}C_{v}&=&C_{2v}+\mathcal{A} C_{v}\\
T_{32}C_{v}&=&C_{32v}+\mathcal{A} C_{2v}\\
T_{132}C_{v}&=&C_{132v}+ \mathcal{A} C_{32v}+\mathcal{A} C_{12v}+\mathcal{A} C_{2v}+ \mathcal{A} C_{v}\\
T_{2132}C_{v}&=&C_{2132v}+ \mathcal{A} C_{212v}+\mathcal{A} C_{132v}+\mathcal{A} C_{32v}+\mathcal{A} C_{12v}+\mathcal{A} C_{2v}+ \mathcal{A} C_{v}+\mathcal{A} C_{v_{3}}\\
T_{12132}C_{v}&=&C_{12132v}+ \mathcal{A} C_{2132v}+\mathcal{A} C_{212v}+\mathcal{A} C_{32v}+\mathcal{A} C_{12v}+\mathcal{A} C_{2v}\\
&&+ \mathcal{A} C_{v}+\mathcal{A} C_{u_{4}}+\mathcal{A} C_{v_{3}}\\
T_{212132}C_{v}&=&C_{212132v}+\mathcal{A} C_{12132v}+ \mathcal{A} C_{2132v}+\mathcal{A} C_{212v}+\mathcal{A} C_{32v}\\ &&+\mathcal{A} C_{12v}+\mathcal{A} C_{2v}+ \mathcal{A} C_{v}+\mathcal{A} C_{u_{4}}+\mathcal{A} C_{v_{4}}+\mathcal{A} C_{v_{3}}+\mathcal{A} C_{v_{2}}\\
T_{1212132}C_{v}&=&T_{212123}C_{v_{3}}+\mathcal{A} C_{212132v}+\mathcal{A} C_{2132} +\mathcal{A} C_{212v}+\mathcal{A} C_{32v}+\mathcal{A} C_{2v}\\
&& +\mathcal{A} C_{v_{5}}+\mathcal{A} C_{v_{4}}+\mathcal{A} C_{v_{3}}+\mathcal{A} C_{v_{2}}
\end{eqnarray*}
Thus $T_{1212132}C_{u}\in\mathcal{M}$ as desired.\\

\vspace{1cm}

\noindent We prove (2) and (3).
Let $w_{1}=s_{1}s_{2}s_{3}s_{2}s_{1}s_{2}$ and $w_{2}=s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}$. These are both translations. Any element in $X_{v}$ can be written under the form $y_{1}w_{1}^{n}$ or $y_{2}w_{2}^{n}$ (where $y_{1}\in Y(w_{1})$ and $y_{2}\in Y(w_{2})$).
Now we have
$$\begin{array}{rllcc}
T_{s_{2}}C_{v}&\equiv& T_{s_{2}v} &\mod \mathcal{H}_{<0}\\
T_{s_{1}s_{2}}C_{v}&\equiv& T_{s_{1}s_{2}v} & \mod \mathcal{H}_{<0}\\
T_{s_{2}s_{1}s_{2}}C_{v}&\equiv& T_{s_{2}s_{1}s_{2}v}+T_{v_{3}}& \mod \mathcal{H}_{<0}\\
T_{s_{3}s_{2}s_{1}s_{2}}C_{v}&\equiv& T_{s_{3}s_{2}s_{1}s_{2}v}+T_{s_{3}v_{3}}& \mod \mathcal{H}_{<0}\\
T_{s_{2}s_{3}s_{2}s_{1}s_{2}}C_{v}&\equiv& T_{s_{2}s_{3}s_{2}s_{1}s_{2}v}+T_{s_{2}s_{3}v_{3}}&  \mod \mathcal{H}_{<0}\\
T_{w_{1}}C_{v}&\equiv& T_{w_{1}v}+T_{s_{1}s_{2}s_{3}v_{3}}&  \mod \mathcal{H}_{<0}\\
\end{array}$$
and if $T_{z}$ appears with a non zero coefficient in the expression of $T_{w_{1}}C_{v}$ in the standard basis then $\ell(w_{1}z)=\ell(w_{1})+\ell(z)$. Therefore for all $y_{1}\in Y(w_{1})$ and $n\geq 1$ we have
$$T_{y_{1}w_{1}^{n}}C_{v} \equiv T_{yw_{1}^{n-1}s_{2}s_{1}s_{2}v}+T_{y_{1}w_{1}^{n-1}s_{1}s_{2}s_{3}v_{3}}  \mod \mathcal{H}_{<0}.$$
Next we have
$$\begin{array}{rllcc}
T_{s_{2}}C_{v}&\equiv& T_{s_{2}v} &\mod \mathcal{H}_{<0}\\
T_{s_{3}s_{2}}C_{v}&\equiv& T_{s_{3}s_{2}v} & \mod \mathcal{H}_{<0}\\
T_{s_{1}s_{3}s_{2}}C_{v}&\equiv& T_{s_{1}s_{3}s_{2}v}& \mod \mathcal{H}_{<0}\\
T_{s_{2}s_{1}s_{3}s_{2}}C_{v}&\equiv&T_{s_{2}s_{1}s_{3}s_{2}v}& \mod \mathcal{H}_{<0}\\
T_{s_{1}s_{2}s_{1}s_{3}s_{2}}C_{v}&\equiv& T_{s_{1}s_{2}s_{1}s_{3}s_{2}v} & \mod \mathcal{H}_{<0}\\
T_{s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}}C_{v}&\equiv& T_{s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}v}& \mod \mathcal{H}_{<0}\\
T_{s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}}C_{v}&\equiv&  T_{s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}v}& \mod \mathcal{H}_{<0}\\
T_{w_{2}s_{3}s_{2}}C_{v}&\equiv& T_{w_{2}v}+T_{s_{3}s_{2}s_{1}s_{2}s_{3}v_{3}} & \mod \mathcal{H}_{<0}\\
\end{array}$$
and if $T_{z}$ appears with a non zero coefficient in the expression of $T_{w_{2}s_{3}s_{2}}C_{v}$ in the standard basis then $\ell(w_{2}z)=\ell(w_{2})+\ell(z)$.  Therefore for all $y_{2}\in Y(w_{2})$ and $n\geq 1$ we have
$$T_{y_{2}w_{2}^{n}s_{3}s_{2}}C_{v} \equiv T_{y_{2}w_{2}^{n-1}s_{2}s_{1}s_{2}v}+T_{y_{2}w_{2}^{n-1}s_{3}s_{2}s_{1}s_{2}s_{3}v_{3}}  \mod \mathcal{H}_{<0}.$$
Let $y\in Y_{v}$ and let $y_{0}=ys_{2}s_{1}s_{2}$. Using the previous equalities, we obtain that
$$T_{y}C_{v}\equiv T_{yv}+T_{y_{0}v_{3}} \mod \mathcal{H}_{<0}.$$
and for $x\in X_{v}-Y_{v}$ we have
$$T_{y}C_{v}\equiv T_{yv} \mod \mathcal{H}_{<0}.$$
Finally using the fact that $p^{*}_{xu,yv}\in\mathcal{A}_{<0}$ we get
$$
\begin{array}{rllll}
\tilde{C_{yv}}&=&T_{y}C_{v}+\underset{xu\sqsubset yv}{\underset{u\in U, x\in X_{u}}{\sum}}p^{*}_{xu,yv}T_{x}C_{u}&\\
&=&T_{y}C_{v}+\underset{x< y,x\in X_{v}}{\sum}p^{*}_{xv,yv}T_{x}C_{v}+ \underset{u\neq v}{\underset{u\in U, x\in X_{u}}{\sum}}p^{*}_{xu,yv}T_{x}C_{u}&\\
&=&T_{y}C_{v} \qquad\qquad\qquad\qquad\qquad\qquad\  &\text{mod $\mathcal{H}_{<0}$}\\
&=&T_{yv}+T_{y_{0}v_{3}}& \text{mod $\mathcal{H}_{<0}$}\\
\end{array}
$$
as required.

\newpage

\section{Proof of \cite[Theorem 5.1]{jeju4} for $\tilde{G}_{2}$}
\label{sec2}

We keep the notation of \cite{jeju4}.\\

\noindent
Let $(W,S)$ be the affine Weyl group of type $\tilde{G}_{2}$ with diagram and weight function given by
\begin{center}
\begin{picture}(150,32)
\put( 40, 10){\circle{10}}
\put( 44,  7){\line(1,0){33}}
\put( 45,  10){\line(1,0){30.5}}
\put( 44, 13){\line(1,0){33}}
\put( 81, 10){\circle{10}}
\put( 86, 10){\line(1,0){29}}
\put(120, 10){\circle{10}}
\put( 38, 20){$a$}
\put( 78, 20){$b$}
\put(118, 20){$b$}
\put( 38, -3){$s_{1}$}
\put( 78, -3){$s_{2}$}
\put(118,-3){$s_{3}$}
\end{picture}
\end{center}
where $a,b$ are positive integers. The partition of $W$ into cells only depends on the ratio $r=a/b$. The aim of this section is to give some details in the computation involved in \cite[Theorem 5.1]{jeju4}. Recall that in \cite{jeju4} we showed that the partition of $W$ given in \cite[Conjecture 3.3]{jeju4} is constant whether
\begin{itemize}
\item $r>2$
\item $r=2$
\item $2>r>3/2$
\item $r=3/2$
\item $3/2>r>1$
\item $r=1$
\item $r<1$
\end{itemize}

Fix $r>0$. Let $\tilde{c}_{0},\ldots,\tilde{c}_{n}$ the sets obtained using the algorithm presented in \cite[\S 3]{jeju4}. Then we denote by
\begin{itemize}
\item $\tilde{c}_{i}^{j}$ the left-connected components lying in $\tilde{c}_{i}$;
\item $u_{i}^{j}$ the element of minimal length lying in $\tilde{c}_{i}^{j}$;
\item $U$ the set which consists of all the $u_{i}^{j}$.
\end{itemize}
Let $u_{i}^{j}\in U$. We set
$$X_{u_{i}^{j}}:=\{w\in W| wu^{j}_{i}\in \tilde{c}^{j}_{i}\}.$$
For each value of $r$ we give
\begin{enumerate}
\item the Hasse diagram of the pre-order $\preceq$ on $U$, which is also the left order on the left cells;
\item A table where for $u\in U$ and $x\in X_{u}$ we put the expression
$$T_{yv}+\sum_{xu\sqsubset yv} a_{xu,yv}T_{x}C_{u}$$
such that
$$T_{y}C_{v}\equiv T_{yv}+\sum_{xu\sqsubset yv} a_{xu,yv}T_{x}C_{u} \mod \mathcal{H}_{<0} .$$
\begin{Rem}
When $T_{x}C_{u}\equiv T_{xu} \mod \mathcal{H}_{<0}$ we do not put it in the table.
\end{Rem}
\end{enumerate}

\noindent
For $w\in W$ we set
$$Y(w)=\{y\in W| \ell(wy^{-1})=\ell(w)-\ell(y)\}.$$

\newpage

\begin{longlist}

\item {\bf Case ${\bf r>2}$.}\\

\begin{center}
\begin{pspicture}(-6,-10)(6,9)
\psset{unit=1.3cm}

\SpecialCoor
\psline(0,-6)(0,6)
\multido{\n=1+1}{7}{
\psline(\n;30)(\n;330)}
\rput(1;30){\psline(0,0)(0,5.5)}
\rput(1;330){\psline(0,0)(0,-5.5)}
\rput(2;30){\psline(0,0)(0,5)}
\rput(2;330){\psline(0,0)(0,-5)}
\rput(3;30){\psline(0,0)(0,4.5)}
\rput(3;330){\psline(0,0)(0,-4.5)}
\rput(4;30){\psline(0,0)(0,4)}
\rput(4;330){\psline(0,0)(0,-4)}
\rput(5;30){\psline(0,0)(0,3.5)}
\rput(5;330){\psline(0,0)(0,-3.5)}
\rput(6;30){\psline(0,0)(0,3)}
\rput(6;330){\psline(0,0)(0,-3)}
\rput(7;30){\psline(0,0)(0,2.5)}
\rput(7;330){\psline(0,0)(0,-2.5)}
\multido{\n=1+1}{7}{
\psline(\n;150)(\n;210)}
\rput(1;150){\psline(0,0)(0,5.5)}
\rput(1;210){\psline(0,0)(0,-5.5)}
\rput(2;150){\psline(0,0)(0,5)}
\rput(2;210){\psline(0,0)(0,-5)}
\rput(3;150){\psline(0,0)(0,4.5)}
\rput(3;210){\psline(0,0)(0,-4.5)}
\rput(4;150){\psline(0,0)(0,4)}
\rput(4;210){\psline(0,0)(0,-4)}
\rput(5;150){\psline(0,0)(0,3.5)}
\rput(5;210){\psline(0,0)(0,-3.5)}
\rput(6;150){\psline(0,0)(0,3)}
\rput(6;210){\psline(0,0)(0,-3)}
\rput(7;150){\psline(0,0)(0,2.5)}
\rput(7;210){\psline(0,0)(0,-2.5)}
\multido{\n=1.5+1.5}{4}{
\psline(-6.062,\n)(6.062,\n)}
\multido{\n=0+1.5}{5}{
\psline(-6.062,-\n)(6.062,-\n)}
\psline(0;0)(7;30)

\rput(0,1){\psline(0;0)(7;30)}
\rput(0,1){\psline(0;0)(7;210)}
\rput(0,2){\psline(0;0)(7;30)}
\rput(0,2){\psline(0;0)(7;210)}
\rput(0,3){\psline(0;0)(6;30)}
\rput(0,3){\psline(0;0)(7;210)}
\rput(0,4){\psline(0;0)(4;30)}
\rput(0,4){\psline(0;0)(7;210)}
\rput(0,5){\psline(0;0)(2;30)}
\rput(0,5){\psline(0;0)(7;210)}
\rput(0,6){\psline(0;0)(7;210)}
\rput(-1.732,6){\psline(0;0)(5;210)}
\rput(-3.464,6){\psline(0;0)(3;210)}
\rput(-5.196,6){\psline(0;0)(1;210)}

\rput(0,-1){\psline(0;0)(7;30)}
\rput(0,-1){\psline(0;0)(7;210)}
\rput(0,-2){\psline(0;0)(7;30)}
\rput(0,-2){\psline(0;0)(7;210)}
\rput(0,-3){\psline(0;0)(7;30)}
\rput(0,-3){\psline(0;0)(6;210)}
\rput(0,-4){\psline(0;0)(7;30)}
\rput(0,-4){\psline(0;0)(4;210)}
\rput(0,-5){\psline(0;0)(7;30)}
\rput(0,-5){\psline(0;0)(2;210)}
\rput(0,-6){\psline(0;0)(7;30)}
\rput(1.732,-6){\psline(0;0)(5;30)}
\rput(3.464,-6){\psline(0;0)(3;30)}
\rput(5.196,-6){\psline(0;0)(1;30)}

\psline(0;0)(6.928;60)
\rput(1.732,0){\psline(0;0)(6.928;60)}
\rput(3.464,0){\psline(0;0)(5.196;60)}
\rput(5.196,0){\psline(0;0)(1.732;60)}
\rput(1.732,0){\psline(0;0)(6.928;240)}
\rput(3.464,0){\psline(0;0)(6.928;240)}
\rput(5.196,0){\psline(0;0)(6.928;240)}
\rput(6.062,-1.5){\psline(0;0)(5.196;240)}
\rput(6.062,-4.5){\psline(0;0)(1.732;240)}
\rput(-1.732,0){\psline(0;0)(6.928;60)}
\rput(-3.464,0){\psline(0;0)(6.928;60)}
\rput(-5.196,0){\psline(0;0)(6.928;60)}
\rput(-1.732,0){\psline(0;0)(6.928;240)}
\rput(-3.464,0){\psline(0;0)(5.196;240)}
\rput(-5.196,0){\psline(0;0)(1.732;240)}
\rput(-6.062,1.5){\psline(0;0)(5.196;60)}
\rput(-6.062,4.5){\psline(0;0)(1.732;60)}

\psline(0;0)(6.928;120)
\psline(0;0)(6.928;300)
\rput(-1.732,0){\psline(0;0)(6.928;120)}
\rput(-3.464,0){\psline(0;0)(5.196;120)}
\rput(-5.196,0){\psline(0;0)(1.732;120)}
\rput(-1.732,0){\psline(0;0)(6.928;300)}
\rput(-3.464,0){\psline(0;0)(6.928;300)}
\rput(-5.196,0){\psline(0;0)(6.928;300)}
\rput(-6.062,-1.5){\psline(0;0)(5.196;300)}
\rput(-6.062,-4.5){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;300)}
\rput(3.464,0){\psline(0;0)(5.196;300)}
\rput(5.196,0){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;120)}
\rput(3.464,0){\psline(0;0)(6.928;120)}
\rput(5.196,0){\psline(0;0)(6.928;120)}
\rput(6.062,1.5){\psline(0;0)(5.196;120)}
\rput(6.062,4.5){\psline(0;0)(1.732;120)}

\rput(0,1){\psline(0;0)(7;150)}
\rput(0,1){\psline(0;0)(7;330)}
\rput(0,2){\psline(0;0)(7;150)}
\rput(0,2){\psline(0;0)(7;330)}
\rput(0,3){\psline(0;0)(6;150)}
\rput(0,3){\psline(0;0)(7;330)}
\rput(0,4){\psline(0;0)(4;150)}
\rput(0,4){\psline(0;0)(7;330)}
\rput(0,5){\psline(0;0)(7;330)}
\rput(0,6){\psline(0;0)(7;330)}
\rput(-1.732,6){\psline(0;0)(2;330)}

\rput(0,-1){\psline(0;0)(7;150)}
\rput(0,-1){\psline(0;0)(7;330)}
\rput(0,-2){\psline(0;0)(7;150)}
\rput(0,-2){\psline(0;0)(7;330)}
\rput(0,-3){\psline(0;0)(7;150)}
\rput(0,-3){\psline(0;0)(6;330)}
\rput(0,-4){\psline(0;0)(7;150)}
\rput(0,-4){\psline(0;0)(4;330)}
\rput(0,-5){\psline(0;0)(7;150)}
\rput(0,-5){\psline(0;0)(2;330)}
\rput(0,-6){\psline(0;0)(7;150)}

\rput(6.062,3.5){\psline(0;0)(5;150)}
\rput(6.062,4.5){\psline(0;0)(3;150)}
\rput(6.062,5.5){\psline(0;0)(1;150)}

\rput(-6.062,-3.5){\psline(0;0)(5;330)}
\rput(-6.062,-4.5){\psline(0;0)(3;330)}
\rput(-6.062,-5.5){\psline(0;0)(1;330)}

\psline(0;0)(7;330)
\psline(0;0)(7;150)
\psline(0;0)(7;210)
\psline(0;0)(6.928;240)

\psline[linewidth=1mm](0,1)(0,1.5)
\psline[linewidth=1mm](0,1)(.433,.75)
\psline[linewidth=1mm](0,0)(.866,1.5)
\psline[linewidth=1mm](.866,1.5)(0,1.5)
\psline[linewidth=1mm](-.866,1.5)(0,1)
\psline[linewidth=1mm](0,1)(0,0)
\psline[linewidth=1mm](0,0)(-.866,1.5)

\psline[linewidth=1mm](0,1.5)(0,3)
\psline[linewidth=1mm](0,3)(-1.732,6)
\psline[linewidth=1mm](-.866,1.5)(-3.464,6)

\psline[linewidth=1mm](.433,.75)(1.732,0)
\psline[linewidth=1mm](1.732,0)(6.062,0)
\psline[linewidth=1mm](2.598,1.5)(6.062,1.5)

\psline[linewidth=1mm](-.433,.75)(-1.732,0)
\psline[linewidth=1mm](-1.732,0)(-6.062,0)
\psline[linewidth=1mm](-2.598,1.5)(-6.062,1.5)

\psline[linewidth=1mm](.866,0)(.866,-1.5)
\psline[linewidth=1mm](.866,-1.5)(3.464,-6)
\psline[linewidth=1mm](.866,0)(1.732,0)
\psline[linewidth=1mm](2.598,-1.5)(5.196,-6)

\psline[linewidth=1mm](-.866,0)(-.866,-1.5)
\psline[linewidth=1mm](-.866,-1.5)(-3.464,-6)
\psline[linewidth=1mm](-.866,0)(-1.732,0)
\psline[linewidth=1mm](-2.598,-1.5)(-5.196,-6)

\psline[linewidth=1mm](.433,2.25)(0,3)
\psline[linewidth=1mm](0.866,4.5)(1.732,6)
\psline[linewidth=1mm](.433,2.25)(1.732,3)
\psline[linewidth=1mm](1.732,3)(3.464,6)

\psline[linewidth=1mm](0,0)(0,-6)
\psline[linewidth=1mm](0,0)(.866,-1.5)
\psline[linewidth=1mm](.866,-1.5)(.866,-6)

\psline[linewidth=1mm](1.732,0)(6.062,-2.5)
\psline[linewidth=1mm](2.598,-1.5)(6.062,-3.5)

\psline[linewidth=1mm](-1.732,0)(-6.062,-2.5)
\psline[linewidth=1mm](-2.598,-1.5)(-6.062,-3.5)

\psline[linewidth=1mm](.866,1.5)(6.062,4.5)
\psline[linewidth=1mm](2.598,1.5)(6.062,3.5)

\psline[linewidth=1mm](-.866,1.5)(-6.062,4.5)
\psline[linewidth=1mm](-2.598,1.5)(-6.062,3.5)

\psline[linewidth=1mm](0,3)(0,6)
\psline[linewidth=1mm](.866,4.5)(.866,6)

\psline[linewidth=1mm](.866,1.5)(1.732,3)
\psline[linewidth=1mm](0,0)(-.866,-1.5)

\psline[linewidth=1mm](0,1.5)(-.866,1.5)

\psline[linewidth=1mm](1.732,0)(2.598,-1.5)
\psline[linewidth=1mm](.866,1.5)(2.598,1.5)
\psline[linewidth=1mm](-.866,1.5)(-2.598,1.5)
\psline[linewidth=1mm](-1.732,0)(-2.598,-1.5)
\psline[linewidth=1mm](0,3)(.866,4.5)

\rput(0,-7){\textsc{Figure 2}. Partition of $\tilde{G}_{2}$ into cells.}

\rput(-1.5,-4.33){{\small ${\bf \tilde{c}_{0}^{1}}$}}
\rput(1.988,-4.31){{\small ${\bf \tilde{c}_{0}^{2}}$}}
\rput(5.452,-4.31){{\small ${\bf \tilde{c}_{0}^{3}}$}}
\rput(5.452,-1.31){{\small ${\bf \tilde{c}_{0}^{4}}$}}
\rput(3.69,1.7){{\small ${\bf \tilde{c}_{0}^{5}}$}}
\rput(2.824,3.2){{\small ${\bf \tilde{c}_{0}^{6}}$}}
\rput(1.1,5.75){{\small ${\bf \tilde{c}_{0}^{7}}$}}
\rput(-0.23,4.67){{\small ${\bf \tilde{c}_{0}^{8}}$}}
\rput(-2.372,3.2){{\small ${\bf \tilde{c}_{0}^{9}}$}}
\rput(-4.97,1.7){{\small ${\bf \tilde{c}_{0}^{10}}$}}

\rput(-4.97,-1.3){{\small ${\bf \tilde{c}_{0}^{11}}$}}
\rput(-4.97,-4.3){{\small ${\bf \tilde{c}_{0}^{12}}$}}

\rput(2.3,-2.33){{\small ${\bf  \tilde{c}_{2}^{1}}$}}
\rput(3.2,.73){{\small ${\bf \tilde{c}_{2}^{2}}$}}
\rput(1.5,4.34){{\small ${\bf \tilde{c}_{2}^{3}}$}}
\rput(-1.5,4.34){{\small ${\bf \tilde{c}_{2}^{4}}$}}
\rput(-3.2,.73){{\small ${\bf \tilde{c}_{2}^{5}}$}}
\rput(-2.3,-2.33){{\small ${\bf  \tilde{c}_{2}^{6}}$}}

\rput(0.3,-4.33){{\small ${\bf  \tilde{c}_{1}^{1}}$}}
\rput(3.2,-1.33){{\small ${\bf \tilde{c}_{1}^{2}}$}}
\rput(3.2,2.34){{\small ${\bf \tilde{c}_{1}^{3}}$}}
\rput(0.3,4.33){{\small ${\bf \tilde{c}_{1}^{4}}$}}
\rput(-3.4,2.34){{\small ${\bf \tilde{c}_{1}^{5}}$}}
\rput(-3.2,-1.33){{\small ${\bf \tilde{c}_{1}^{6}}$}}

\rput(-.22,1.3){{\small ${\bf \tilde{c}_{4}^{1}}$}}

\rput(.6,.19){{\small ${\bf \tilde{c}_{3}^{1}}$}}
\rput(.4,1.93){{\small ${\bf \tilde{c}_{3}^{2}}$}}
\rput(-.49,.23){{\small ${\bf \tilde{c}_{3}^{3}}$}}

\rput(.3,1.1){{\small ${\bf \tilde{c}_{5}^{1}}$}}
\rput(-.23,.73){{\small ${\bf \tilde{c}_{5}^{2}}$}}

\rput(.17,.68){{\small ${\bf \tilde{c}_{6}^{1}}$}}

\end{pspicture}
\end{center}

\newpage

In the following Hasse diagram, the black edges hold for all $r>2$, the green edges only hold for $3<r\leq 4$ and the red edges only hold for  $2<r\leq 3$.

\begin{center}
\begin{pspicture}(-1.3,-1.5)(13,13)
\psset{unit=.7pt}

\pscircle(-100,0){10}
\rput(-100,0){{\small $u_{0}^{1}$}}
\pscircle(-60,0){10}
\rput(-60,0){{\small $u_{0}^{2}$}}

\pscircle(0,0){10}
\rput(0,0){{\small $u_{0}^{3}$}}
\pscircle(40,0){10}
\rput(40,0){{\small $u_{0}^{4}$}}
\pscircle(100,0){10}
\rput(100,0){{\small $u_{0}^{5}$}}
\pscircle(140,0){10}
\rput(140,0){{\small $u_{0}^{6}$}}

\pscircle(200,0){10}
\rput(200,0){{\small $u_{0}^{7}$}}
\pscircle(240,0){10}
\rput(240,0){{\small $u_{0}^{8}$}}

\pscircle(300,0){10}
\rput(300,0){{\small $u_{0}^{9}$}}
\pscircle(340,0){10}
\rput(340,0){{\small $u_{0}^{10}$}}

\pscircle(400,0){10}
\rput(400,0){{\small $u_{0}^{11}$}}
\pscircle(440,0){10}
\rput(440,0){{\small $u_{0}^{12}$}}

\pscircle(500,0){10}
\rput(500,0){{\small $u_{0}^{1}$}}
\pscircle(540,0){10}
\rput(540,0){{\small $u_{0}^{2}$}}

\pscircle(20,200){10}
\rput(20,200){{\scriptsize $u_{2}^{1}$}}

\pscircle(120,200){10}
\rput(120,200){{\scriptsize $u_{2}^{2}$}}

\pscircle(220,200){10}
\rput(220,200){{\scriptsize $u_{2}^{3}$}}

\pscircle(270,200){10}
\rput(270,200){{\scriptsize $u_{2}^{4}$}}

\pscircle(320,200){10}
\rput(320,200){{\scriptsize $u_{2}^{5}$}}

\pscircle(420,200){10}
\rput(420,200){{\scriptsize $u_{2}^{6}$}}

\pscircle(-80,100){10}
\rput(-80,100){{\scriptsize $u_{1}^{1}$}}

\pscircle(20,100){10}
\rput(20,100){{\scriptsize $u_{1}^{2}$}}

\pscircle(120,100){10}
\rput(120,100){{\scriptsize $u_{1}^{3}$}}

\pscircle(220,100){10}
\rput(220,100){{\scriptsize $u_{1}^{4}$}}

\pscircle(320,100){10}
\rput(320,100){{\scriptsize $u_{1}^{5}$}}

\pscircle(420,100){10}
\rput(420,100){{\scriptsize $u_{1}^{6}$}}

\pscircle(520,100){10}
\rput(520,100){{\scriptsize $u_{1}^{1}$}}

\pscircle(70,300){10}
\rput(70,300){{\tiny $u_{3}^{1}$}}

\pscircle(245,300){10}
\rput(245,300){{\tiny $u_{3}^{2}$}}

\pscircle(370,300){10}
\rput(370,300){{\tiny $u_{3}^{3}$}}

\pscircle(280,400){10}
\rput(280,400){{\scriptsize$u_{5}^{1}$}}

\pscircle(335,400){10}
\rput(335,400){{\scriptsize$u_{5}^{1}$}}

\pscircle(307.5,350){10}
\rput(307.5,350){{\scriptsize$u_{4}^{1}$}}

\pscircle(307.5,450){10}
\rput(307.5,450){{\scriptsize$u_{6}^{1}$}}

\psline(-80,90)(-100,10)
\psline(-80,90)(-60,10)

\psline(20,90)(0,10)
\psline(20,90)(40,10)

\psline(120,90)(100,10)
\psline(120,90)(140,10)

\psline(220,90)(200,10)
\psline(220,90)(240,10)
\psline[linecolor=green](220,90)(140,10)

\psline(320,90)(300,10)
\psline(320,90)(340,10)

\psline(420,90)(400,10)
\psline(420,90)(440,10)
\psline[linecolor=green](420,90)(500,10)

\psline(520,90)(500,10)
\psline(520,90)(540,10)

\psline(220,90)(40,10)

\psline(320,90)(500,10)

\psline(20,190)(20,110)

\psline(120,190)(120,110)

\psline(220,190)(220,110)

\psline(320,190)(320,110)

\psline(420,190)(420,110)

\psline(20,190)(-80,110)

\psline(20,190)(140,10)

\psline(120,190)(40,10)

\psline(220,190)(140,10)

\psline(220,190)(300,10)

\psline(270,190)(240,10)

\psline(270,190)(300,10)

\psline(320,190)(400,10)

\psline(420,190)(300,10)

\psline(420,190)(500,10)

\psline(70,290)(20,210)

\psline(70,290)(120,210)

\psline(245,290)(220,210)

\psline(245,290)(270,210)

\psline(245,290)(120,210)

\psline(370,290)(320,210)

\psline(370,290)(420,210)

\psline(307.5,340)(270,210)

\psline(280,390)(307.5,360)

\psline(280,390)(245,310)

\psline(335,390)(307.5,360)

\psline(335,390)(370,310)

\psline(307.5,440)(70,310)

\psline(307.5,440)(280,410)

\psline(307.5,440)(335,410)

\psline[linewidth=.3mm,linecolor=red](20,90)(-100,10)
\psline[linewidth=.3mm,linecolor=red](220,90)(300,10)
\psline[linewidth=.3mm,linecolor=green](420,90)(500,10)

\rput(250,-50){Figure 3. Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

Let $w=s_{1}s_{2}s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3}$, $w_{1}=s_{1}s_{2}s_{3}s_{2}s_{1}s_{2}$ and $w_{2}=s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}$. In the following table we have
$$y_{1}\in \{yw_{1}^{n}| y\in Y(w_{1}), n\in\mathbb{N}\} \text{ and } y_{2}\in \{yw_{2}^{n}| y\in Y(w_{2})\}$$
$$y\in \{yw^{n}| y\in Y(w), n\in\mathbb{N}\} $$

{\footnotesize
\begin{table}[htbp] \caption{Condition {\bf I5}}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline

u_{1}^{4} & s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b}C_{u_{0}^{6}}\\\hline
u_{1}^{4} & s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b}T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{4} & s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b}T_{s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{4} & s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b}T_{s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{4} & s_{2}s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b}T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{4} & yw & T_{xu} +v^{-a+3b}T_{y}C_{u_{0}^{6}}\\\hline

u_{1}^{6} & s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b}T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b}T_{s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b}T_{s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b}T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & yw & T_{xu} +v^{-a+3b}T_{y}C_{u_{0}^{1}}\\\hline

u_{2}^{3} & s_{2}s_{1}s_{2} & T_{xu} + C_{u_{0}^{6}}\\\hline
u_{2}^{3} & s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{3} & s_{2}s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{3} & y_{1}w_{1} & T_{xu} +T_{y_{1}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline

u_{2}^{3} & y_{2}w_{2}s_{3}s_{2} & T_{xu} +T_{y_{2}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline

u_{2}^{6} & s_{2}s_{1}s_{2} & T_{xu} +C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{2}s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & y_{1}w_{1}& T_{xu} +T_{y_{1}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{6} & y_{2}w_{2}s_{3}s_{2} & T_{xu} +T_{y_{2}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item {\bf Case ${\bf r=2}$}

\begin{center}
\begin{pspicture}(-6,-6)(6,9)
\psset{unit=1.3cm}

\SpecialCoor
\psline(0,-6)(0,6)
\multido{\n=1+1}{7}{
\psline(\n;30)(\n;330)}
\rput(1;30){\psline(0,0)(0,5.5)}
\rput(1;330){\psline(0,0)(0,-5.5)}
\rput(2;30){\psline(0,0)(0,5)}
\rput(2;330){\psline(0,0)(0,-5)}
\rput(3;30){\psline(0,0)(0,4.5)}
\rput(3;330){\psline(0,0)(0,-4.5)}
\rput(4;30){\psline(0,0)(0,4)}
\rput(4;330){\psline(0,0)(0,-4)}
\rput(5;30){\psline(0,0)(0,3.5)}
\rput(5;330){\psline(0,0)(0,-3.5)}
\rput(6;30){\psline(0,0)(0,3)}
\rput(6;330){\psline(0,0)(0,-3)}
\rput(7;30){\psline(0,0)(0,2.5)}
\rput(7;330){\psline(0,0)(0,-2.5)}
\multido{\n=1+1}{7}{
\psline(\n;150)(\n;210)}
\rput(1;150){\psline(0,0)(0,5.5)}
\rput(1;210){\psline(0,0)(0,-5.5)}
\rput(2;150){\psline(0,0)(0,5)}
\rput(2;210){\psline(0,0)(0,-5)}
\rput(3;150){\psline(0,0)(0,4.5)}
\rput(3;210){\psline(0,0)(0,-4.5)}
\rput(4;150){\psline(0,0)(0,4)}
\rput(4;210){\psline(0,0)(0,-4)}
\rput(5;150){\psline(0,0)(0,3.5)}
\rput(5;210){\psline(0,0)(0,-3.5)}
\rput(6;150){\psline(0,0)(0,3)}
\rput(6;210){\psline(0,0)(0,-3)}
\rput(7;150){\psline(0,0)(0,2.5)}
\rput(7;210){\psline(0,0)(0,-2.5)}
\multido{\n=1.5+1.5}{4}{
\psline(-6.062,\n)(6.062,\n)}
\multido{\n=0+1.5}{5}{
\psline(-6.062,-\n)(6.062,-\n)}
\psline(0;0)(7;30)

\rput(0,1){\psline(0;0)(7;30)}
\rput(0,1){\psline(0;0)(7;210)}
\rput(0,2){\psline(0;0)(7;30)}
\rput(0,2){\psline(0;0)(7;210)}
\rput(0,3){\psline(0;0)(6;30)}
\rput(0,3){\psline(0;0)(7;210)}
\rput(0,4){\psline(0;0)(4;30)}
\rput(0,4){\psline(0;0)(7;210)}
\rput(0,5){\psline(0;0)(2;30)}
\rput(0,5){\psline(0;0)(7;210)}
\rput(0,6){\psline(0;0)(7;210)}
\rput(-1.732,6){\psline(0;0)(5;210)}
\rput(-3.464,6){\psline(0;0)(3;210)}
\rput(-5.196,6){\psline(0;0)(1;210)}

\rput(0,-1){\psline(0;0)(7;30)}
\rput(0,-1){\psline(0;0)(7;210)}
\rput(0,-2){\psline(0;0)(7;30)}
\rput(0,-2){\psline(0;0)(7;210)}
\rput(0,-3){\psline(0;0)(7;30)}
\rput(0,-3){\psline(0;0)(6;210)}
\rput(0,-4){\psline(0;0)(7;30)}
\rput(0,-4){\psline(0;0)(4;210)}
\rput(0,-5){\psline(0;0)(7;30)}
\rput(0,-5){\psline(0;0)(2;210)}
\rput(0,-6){\psline(0;0)(7;30)}
\rput(1.732,-6){\psline(0;0)(5;30)}
\rput(3.464,-6){\psline(0;0)(3;30)}
\rput(5.196,-6){\psline(0;0)(1;30)}

\psline(0;0)(6.928;60)
\rput(1.732,0){\psline(0;0)(6.928;60)}
\rput(3.464,0){\psline(0;0)(5.196;60)}
\rput(5.196,0){\psline(0;0)(1.732;60)}
\rput(1.732,0){\psline(0;0)(6.928;240)}
\rput(3.464,0){\psline(0;0)(6.928;240)}
\rput(5.196,0){\psline(0;0)(6.928;240)}
\rput(6.062,-1.5){\psline(0;0)(5.196;240)}
\rput(6.062,-4.5){\psline(0;0)(1.732;240)}
\rput(-1.732,0){\psline(0;0)(6.928;60)}
\rput(-3.464,0){\psline(0;0)(6.928;60)}
\rput(-5.196,0){\psline(0;0)(6.928;60)}
\rput(-1.732,0){\psline(0;0)(6.928;240)}
\rput(-3.464,0){\psline(0;0)(5.196;240)}
\rput(-5.196,0){\psline(0;0)(1.732;240)}
\rput(-6.062,1.5){\psline(0;0)(5.196;60)}
\rput(-6.062,4.5){\psline(0;0)(1.732;60)}

\psline(0;0)(6.928;120)
\psline(0;0)(6.928;300)
\rput(-1.732,0){\psline(0;0)(6.928;120)}
\rput(-3.464,0){\psline(0;0)(5.196;120)}
\rput(-5.196,0){\psline(0;0)(1.732;120)}
\rput(-1.732,0){\psline(0;0)(6.928;300)}
\rput(-3.464,0){\psline(0;0)(6.928;300)}
\rput(-5.196,0){\psline(0;0)(6.928;300)}
\rput(-6.062,-1.5){\psline(0;0)(5.196;300)}
\rput(-6.062,-4.5){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;300)}
\rput(3.464,0){\psline(0;0)(5.196;300)}
\rput(5.196,0){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;120)}
\rput(3.464,0){\psline(0;0)(6.928;120)}
\rput(5.196,0){\psline(0;0)(6.928;120)}
\rput(6.062,1.5){\psline(0;0)(5.196;120)}
\rput(6.062,4.5){\psline(0;0)(1.732;120)}

\rput(0,1){\psline(0;0)(7;150)}
\rput(0,1){\psline(0;0)(7;330)}
\rput(0,2){\psline(0;0)(7;150)}
\rput(0,2){\psline(0;0)(7;330)}
\rput(0,3){\psline(0;0)(6;150)}
\rput(0,3){\psline(0;0)(7;330)}
\rput(0,4){\psline(0;0)(4;150)}
\rput(0,4){\psline(0;0)(7;330)}
\rput(0,5){\psline(0;0)(7;330)}
\rput(0,6){\psline(0;0)(7;330)}
\rput(-1.732,6){\psline(0;0)(2;330)}

\rput(0,-1){\psline(0;0)(7;150)}
\rput(0,-1){\psline(0;0)(7;330)}
\rput(0,-2){\psline(0;0)(7;150)}
\rput(0,-2){\psline(0;0)(7;330)}
\rput(0,-3){\psline(0;0)(7;150)}
\rput(0,-3){\psline(0;0)(6;330)}
\rput(0,-4){\psline(0;0)(7;150)}
\rput(0,-4){\psline(0;0)(4;330)}
\rput(0,-5){\psline(0;0)(7;150)}
\rput(0,-5){\psline(0;0)(2;330)}
\rput(0,-6){\psline(0;0)(7;150)}

\rput(6.062,3.5){\psline(0;0)(5;150)}
\rput(6.062,4.5){\psline(0;0)(3;150)}
\rput(6.062,5.5){\psline(0;0)(1;150)}

\rput(-6.062,-3.5){\psline(0;0)(5;330)}
\rput(-6.062,-4.5){\psline(0;0)(3;330)}
\rput(-6.062,-5.5){\psline(0;0)(1;330)}

\psline(0;0)(7;330)
\psline(0;0)(7;150)
\psline(0;0)(7;210)
\psline(0;0)(6.928;240)

\pspolygon[fillcolor=gray,fillstyle=solid](0,0)(0,1)(0.433,0.75)

\psline[linewidth=1mm](0,1)(0,1.5)
\psline[linewidth=1mm](0,1)(.433,.75)
\psline[linewidth=1mm](0,0)(.866,1.5)
\psline[linewidth=1mm](.866,1.5)(0,1.5)
\psline[linewidth=1mm](-.866,1.5)(0,1)
\psline[linewidth=1mm](0,1)(0,0)
\psline[linewidth=1mm](0,0)(-.866,1.5)

\psline[linewidth=1mm](0,1.5)(0,3)
\psline[linewidth=1mm](0,3)(-1.732,6)
\psline[linewidth=1mm](-.866,1.5)(-3.464,6)

\psline[linewidth=1mm](.433,.75)(1.732,0)
\psline[linewidth=1mm](1.732,0)(6.062,0)
\psline[linewidth=1mm](2.598,1.5)(6.062,1.5)

\psline[linewidth=1mm](-.433,.75)(-1.732,0)
\psline[linewidth=1mm](-1.732,0)(-6.062,0)
\psline[linewidth=1mm](-2.598,1.5)(-6.062,1.5)

\psline[linewidth=1mm](.866,0)(.866,-1.5)
\psline[linewidth=1mm](.866,-1.5)(3.464,-6)
\psline[linewidth=1mm](.866,0)(1.732,0)
\psline[linewidth=1mm](2.598,-1.5)(5.196,-6)

\psline[linewidth=1mm](-.866,0)(-.866,-1.5)
\psline[linewidth=1mm](-.866,-1.5)(-3.464,-6)
\psline[linewidth=1mm](-.866,0)(-1.732,0)
\psline[linewidth=1mm](-2.598,-1.5)(-5.196,-6)

\psline[linewidth=1mm](.433,2.25)(0,3)
\psline[linewidth=1mm](0.866,4.5)(1.732,6)
\psline[linewidth=1mm](.433,2.25)(1.732,3)
\psline[linewidth=1mm](1.732,3)(3.464,6)

\psline[linewidth=1mm](0,0)(0,-6)
\psline[linewidth=1mm](0,0)(.866,-1.5)
\psline[linewidth=1mm](.866,-1.5)(.866,-6)

\psline[linewidth=1mm](1.732,0)(6.062,-2.5)
\psline[linewidth=1mm](2.598,-1.5)(6.062,-3.5)

\psline[linewidth=1mm](-1.732,0)(-6.062,-2.5)
\psline[linewidth=1mm](-2.598,-1.5)(-6.062,-3.5)

\psline[linewidth=1mm](.866,1.5)(6.062,4.5)
\psline[linewidth=1mm](2.598,1.5)(6.062,3.5)

\psline[linewidth=1mm](-.866,1.5)(-6.062,4.5)
\psline[linewidth=1mm](-2.598,1.5)(-6.062,3.5)

\psline[linewidth=1mm](0,3)(0,6)
\psline[linewidth=1mm](.866,4.5)(.866,6)

\psline[linewidth=1mm](.866,1.5)(1.732,3)
\psline[linewidth=1mm](0,0)(-.866,-1.5)

\psline[linewidth=1mm](1.732,0)(2.598,-1.5)
\psline[linewidth=1mm](.866,1.5)(2.598,1.5)
\psline[linewidth=1mm](-.866,1.5)(-2.598,1.5)
\psline[linewidth=1mm](-1.732,0)(-2.598,-1.5)
\psline[linewidth=1mm](0,3)(.866,4.5)

\rput(0,-7){\textsc{Figure 4}. Partition of $\tilde{G}_{2}$ into cells}

\rput(-1.5,-4.33){{\small ${\bf \tilde{c}_{0}^{1}}$}}
\rput(1.988,-4.31){{\small ${\bf \tilde{c}_{0}^{2}}$}}
\rput(5.452,-4.31){{\small ${\bf \tilde{c}_{0}^{3}}$}}
\rput(5.452,-1.31){{\small ${\bf \tilde{c}_{0}^{4}}$}}
\rput(3.69,1.7){{\small ${\bf \tilde{c}_{0}^{5}}$}}
\rput(2.824,3.2){{\small ${\bf \tilde{c}_{0}^{6}}$}}
\rput(1.1,5.75){{\small ${\bf \tilde{c}_{0}^{7}}$}}
\rput(-0.23,4.67){{\small ${\bf \tilde{c}_{0}^{8}}$}}
\rput(-2.372,3.2){{\small ${\bf \tilde{c}_{0}^{9}}$}}
\rput(-4.97,1.7){{\small ${\bf \tilde{c}_{0}^{10}}$}}

\rput(-4.97,-1.3){{\small ${\bf \tilde{c}_{0}^{11}}$}}
\rput(-4.97,-4.3){{\small ${\bf \tilde{c}_{0}^{12}}$}}

\rput(2.3,-2.33){{\small ${\bf  \tilde{c}_{2}^{1}}$}}
\rput(3.2,.73){{\small ${\bf \tilde{c}_{2}^{2}}$}}
\rput(1.5,4.34){{\small ${\bf \tilde{c}_{2}^{3}}$}}
\rput(-1.5,4.34){{\small ${\bf \tilde{c}_{2}^{4}}$}}
\rput(-3.2,.73){{\small ${\bf \tilde{c}_{2}^{5}}$}}
\rput(-2.3,-2.33){{\small ${\bf  \tilde{c}_{2}^{6}}$}}

\rput(0.3,-4.33){{\small ${\bf  \tilde{c}_{1}^{1}}$}}
\rput(3.2,-1.33){{\small ${\bf \tilde{c}_{1}^{2}}$}}
\rput(3.2,2.34){{\small ${\bf \tilde{c}_{1}^{3}}$}}
\rput(0.3,4.33){{\small ${\bf \tilde{c}_{1}^{4}}$}}
\rput(-3.4,2.34){{\small ${\bf \tilde{c}_{1}^{5}}$}}
\rput(-3.2,-1.33){{\small ${\bf \tilde{c}_{1}^{6}}$}}

\rput(.6,.19){{\small ${\bf \tilde{c}_{4}^{1}}$}}
\rput(.4,1.93){{\small ${\bf \tilde{c}_{4}^{2}}$}}
\rput(-.49,.23){{\small ${\bf \tilde{c}_{4}^{3}}$}}

\rput(.3,1.1){{\small ${\bf \tilde{c}_{5}^{1}}$}}
\rput(-.23,.73){{\small ${\bf \tilde{c}_{5}^{2}}$}}

\rput(.17,.68){{\small ${\bf \tilde{c}_{6}^{1}}$}}

\end{pspicture}
\end{center}

\newpage

\begin{center}
\begin{pspicture}(-1.3,-1.5)(13,13)
\psset{unit=.7pt}

\pscircle(-100,0){10}
\rput(-100,0){{\small $u_{0}^{1}$}}
\pscircle(-60,0){10}
\rput(-60,0){{\small $u_{0}^{2}$}}

\pscircle(0,0){10}
\rput(0,0){{\small $u_{0}^{3}$}}
\pscircle(40,0){10}
\rput(40,0){{\small $u_{0}^{4}$}}
\pscircle(100,0){10}
\rput(100,0){{\small $u_{0}^{5}$}}
\pscircle(140,0){10}
\rput(140,0){{\small $u_{0}^{6}$}}

\pscircle(200,0){10}
\rput(200,0){{\small $u_{0}^{7}$}}
\pscircle(240,0){10}
\rput(240,0){{\small $u_{0}^{8}$}}

\pscircle(300,0){10}
\rput(300,0){{\small $u_{0}^{9}$}}
\pscircle(340,0){10}
\rput(340,0){{\small $u_{0}^{10}$}}

\pscircle(400,0){10}
\rput(400,0){{\small $u_{0}^{11}$}}
\pscircle(440,0){10}
\rput(440,0){{\small $u_{0}^{12}$}}

\pscircle(500,0){10}
\rput(500,0){{\small $u_{0}^{1}$}}
\pscircle(540,0){10}
\rput(540,0){{\small $u_{0}^{2}$}}

\pscircle(20,200){10}
\rput(20,200){{\scriptsize $u_{2}^{1}$}}

\pscircle(120,200){10}
\rput(120,200){{\scriptsize $u_{2}^{2}$}}

\pscircle(220,200){10}
\rput(220,200){{\scriptsize $u_{2}^{3}$}}

\pscircle(270,200){10}
\rput(270,200){{\scriptsize $u_{2}^{4}$}}

\pscircle(320,200){10}
\rput(320,200){{\scriptsize $u_{2}^{5}$}}

\pscircle(420,200){10}
\rput(420,200){{\scriptsize $u_{2}^{6}$}}

\pscircle(-80,100){10}
\rput(-80,100){{\scriptsize $u_{1}^{1}$}}

\pscircle(20,100){10}
\rput(20,100){{\scriptsize $u_{1}^{2}$}}

\pscircle(120,100){10}
\rput(120,100){{\scriptsize $u_{1}^{3}$}}

\pscircle(220,100){10}
\rput(220,100){{\scriptsize $u_{1}^{4}$}}

\pscircle(320,100){10}
\rput(320,100){{\scriptsize $u_{1}^{5}$}}

\pscircle(420,100){10}
\rput(420,100){{\scriptsize $u_{1}^{6}$}}

\pscircle(520,100){10}
\rput(520,100){{\scriptsize $u_{1}^{1}$}}

\pscircle(70,300){10}
\rput(70,300){{\tiny $u_{4}^{1}$}}

\pscircle(245,300){10}
\rput(245,300){{\tiny $u_{4}^{2}$}}

\pscircle(370,300){10}
\rput(370,300){{\tiny $u_{4}^{3}$}}

\pscircle(280,400){10}
\rput(280,400){{\scriptsize$u_{5}^{1}$}}

\pscircle(335,400){10}
\rput(335,400){{\scriptsize$u_{5}^{2}$}}

\pscircle(307.5,350){3}

\pscircle(307.5,450){10}
\rput(307.5,450){{\scriptsize$u_{6}^{1}$}}

\psline(-80,90)(-100,10)
\psline(-80,90)(-60,10)

\psline(20,90)(0,10)
\psline(20,90)(40,10)

\psline(20,90)(-100,10)

\psline(20,90)(-60,10)

\psline(20,90)(140,10)

\psline(120,90)(100,10)
\psline(120,90)(140,10)

\psline(120,90)(40,10)

\psline(220,90)(200,10)
\psline(220,90)(240,10)

\psline(220,90)(300,10)

\psline(320,90)(300,10)
\psline(320,90)(340,10)

\psline(320,90)(400,10)

\psline(420,90)(400,10)
\psline(420,90)(440,10)

\psline(420,90)(300,10)

\psline(520,90)(500,10)
\psline(520,90)(540,10)

\psline(220,90)(40,10)

\psline(220,90)(140,10)

\psline(320,90)(500,10)

\psline(420,90)(500,10)

\psline(20,190)(20,110)

\psline(120,190)(120,110)

\psline(220,190)(220,110)

\psline(320,190)(320,110)

\psline(420,190)(420,110)

\psline(20,190)(-80,110)

\psline(270,190)(240,10)

\psline(270,190)(300,10)

\psline(70,290)(20,210)

\psline(70,290)(120,210)

\psline(245,290)(220,210)

\psline(245,290)(270,210)

\psline(245,290)(120,210)

\psline(370,290)(320,210)

\psline(370,290)(420,210)

\psline(280,390)(245,310)

\psline(280,390)(307.5,353)
\psline(307.5,347)(270,210)
\psline(335,390)(307.5,353)

\psline(335,390)(370,310)

\psline(307.5,440)(70,310)

\psline(307.5,440)(280,410)

\psline(307.5,440)(335,410)

\rput(250,-50){Figure 5. Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

Let $w=s_{1}s_{2}s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3}$, $w_{1}=s_{1}s_{2}s_{3}s_{2}s_{1}s_{2}$ and $w_{2}=s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}$. In the following table we have
$$y\in \{zw^{n}| z\in Y(w), n\in\mathbb{N}\} $$
$$y_{1}\in \{yw_{1}^{n}| y\in Y(w_{1}), n\in\mathbb{N}\} \text{ and } y_{2}\in \{yw_{2}^{n}| y\in Y(w_{2})\}$$

{\footnotesize
\begin{table}[htbp] \caption{Condition {\bf I5} for $r=2$}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{1}^{2} & ys_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} + T_{y}C_{u_{0}^{1}}\\\hline

u_{1}^{4} & s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v C_{u_{0}^{6}}-C_{u_{0}^{9}}\\\hline
u_{1}^{4} & s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu}+v T_{s_{3}}C_{u_{0}^{6}}-T_{s_{3}}C_{u_{0}^{9}}\\\hline
u_{1}^{4} & s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} &
T_{xu} +v T_{s_{2}s_{3}}C_{u_{0}^{6}}-T_{s_{2}s_{3}}C_{u_{0}^{9}}\\\hline
u_{1}^{4} & s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} &
T_{xu} +v T_{s_{1}s_{2}s_{3}}C_{u_{0}^{6}}-T_{s_{1}s_{2}s_{3}}C_{u_{0}^{9}}\\\hline
u_{1}^{4} & s_{2}s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} &
T_{xu} +v T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}-T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{9}}\\\hline
u_{1}^{4} & yw &
T_{xu} +v T_{ys_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}- T_{ys_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}-T_{ys_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{9}}\\\hline

u_{1}^{6} & s_{2}s_{1}s_{2}s_{1} & T_{xu} +v C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v T_{s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v T_{s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & yw &
T_{xu} +v T_{ys_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}-T_{ys_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{3} & s_{2}s_{1}s_{2} & T_{xu} + C_{u_{0}^{6}}\\\hline
u_{2}^{3} & s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{3} & s_{2}s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{3} & y_{1}w_{1} & T_{xu} +T_{y_{1}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline

u_{2}^{3} & y_{2}w_{2}s_{3}s_{2} & T_{xu} +T_{y_{2}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline

u_{2}^{6} & s_{2}s_{1}s_{2} & T_{xu} +C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{2}s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & y_{1}w_{1} & T_{xu} +T_{y_{1}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u^{6}_{2} & y_{2}w_{2}s_{3}s_{2} & T_{xu} +T_{y_{2}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item {\bf Case ${\bf 3/2<r<2}$}

\begin{center}
\begin{pspicture}(-6,-6)(6,9)
\psset{unit=1.3cm}

\SpecialCoor
\psline(0,-6)(0,6)
\multido{\n=1+1}{7}{
\psline(\n;30)(\n;330)}
\rput(1;30){\psline(0,0)(0,5.5)}
\rput(1;330){\psline(0,0)(0,-5.5)}
\rput(2;30){\psline(0,0)(0,5)}
\rput(2;330){\psline(0,0)(0,-5)}
\rput(3;30){\psline(0,0)(0,4.5)}
\rput(3;330){\psline(0,0)(0,-4.5)}
\rput(4;30){\psline(0,0)(0,4)}
\rput(4;330){\psline(0,0)(0,-4)}
\rput(5;30){\psline(0,0)(0,3.5)}
\rput(5;330){\psline(0,0)(0,-3.5)}
\rput(6;30){\psline(0,0)(0,3)}
\rput(6;330){\psline(0,0)(0,-3)}
\rput(7;30){\psline(0,0)(0,2.5)}
\rput(7;330){\psline(0,0)(0,-2.5)}
\multido{\n=1+1}{7}{
\psline(\n;150)(\n;210)}
\rput(1;150){\psline(0,0)(0,5.5)}
\rput(1;210){\psline(0,0)(0,-5.5)}
\rput(2;150){\psline(0,0)(0,5)}
\rput(2;210){\psline(0,0)(0,-5)}
\rput(3;150){\psline(0,0)(0,4.5)}
\rput(3;210){\psline(0,0)(0,-4.5)}
\rput(4;150){\psline(0,0)(0,4)}
\rput(4;210){\psline(0,0)(0,-4)}
\rput(5;150){\psline(0,0)(0,3.5)}
\rput(5;210){\psline(0,0)(0,-3.5)}
\rput(6;150){\psline(0,0)(0,3)}
\rput(6;210){\psline(0,0)(0,-3)}
\rput(7;150){\psline(0,0)(0,2.5)}
\rput(7;210){\psline(0,0)(0,-2.5)}
\multido{\n=1.5+1.5}{4}{
\psline(-6.062,\n)(6.062,\n)}
\multido{\n=0+1.5}{5}{
\psline(-6.062,-\n)(6.062,-\n)}
\psline(0;0)(7;30)

\rput(0,1){\psline(0;0)(7;30)}
\rput(0,1){\psline(0;0)(7;210)}
\rput(0,2){\psline(0;0)(7;30)}
\rput(0,2){\psline(0;0)(7;210)}
\rput(0,3){\psline(0;0)(6;30)}
\rput(0,3){\psline(0;0)(7;210)}
\rput(0,4){\psline(0;0)(4;30)}
\rput(0,4){\psline(0;0)(7;210)}
\rput(0,5){\psline(0;0)(2;30)}
\rput(0,5){\psline(0;0)(7;210)}
\rput(0,6){\psline(0;0)(7;210)}
\rput(-1.732,6){\psline(0;0)(5;210)}
\rput(-3.464,6){\psline(0;0)(3;210)}
\rput(-5.196,6){\psline(0;0)(1;210)}

\rput(0,-1){\psline(0;0)(7;30)}
\rput(0,-1){\psline(0;0)(7;210)}
\rput(0,-2){\psline(0;0)(7;30)}
\rput(0,-2){\psline(0;0)(7;210)}
\rput(0,-3){\psline(0;0)(7;30)}
\rput(0,-3){\psline(0;0)(6;210)}
\rput(0,-4){\psline(0;0)(7;30)}
\rput(0,-4){\psline(0;0)(4;210)}
\rput(0,-5){\psline(0;0)(7;30)}
\rput(0,-5){\psline(0;0)(2;210)}
\rput(0,-6){\psline(0;0)(7;30)}
\rput(1.732,-6){\psline(0;0)(5;30)}
\rput(3.464,-6){\psline(0;0)(3;30)}
\rput(5.196,-6){\psline(0;0)(1;30)}

\psline(0;0)(6.928;60)
\rput(1.732,0){\psline(0;0)(6.928;60)}
\rput(3.464,0){\psline(0;0)(5.196;60)}
\rput(5.196,0){\psline(0;0)(1.732;60)}
\rput(1.732,0){\psline(0;0)(6.928;240)}
\rput(3.464,0){\psline(0;0)(6.928;240)}
\rput(5.196,0){\psline(0;0)(6.928;240)}
\rput(6.062,-1.5){\psline(0;0)(5.196;240)}
\rput(6.062,-4.5){\psline(0;0)(1.732;240)}
\rput(-1.732,0){\psline(0;0)(6.928;60)}
\rput(-3.464,0){\psline(0;0)(6.928;60)}
\rput(-5.196,0){\psline(0;0)(6.928;60)}
\rput(-1.732,0){\psline(0;0)(6.928;240)}
\rput(-3.464,0){\psline(0;0)(5.196;240)}
\rput(-5.196,0){\psline(0;0)(1.732;240)}
\rput(-6.062,1.5){\psline(0;0)(5.196;60)}
\rput(-6.062,4.5){\psline(0;0)(1.732;60)}

\psline(0;0)(6.928;120)
\psline(0;0)(6.928;300)
\rput(-1.732,0){\psline(0;0)(6.928;120)}
\rput(-3.464,0){\psline(0;0)(5.196;120)}
\rput(-5.196,0){\psline(0;0)(1.732;120)}
\rput(-1.732,0){\psline(0;0)(6.928;300)}
\rput(-3.464,0){\psline(0;0)(6.928;300)}
\rput(-5.196,0){\psline(0;0)(6.928;300)}
\rput(-6.062,-1.5){\psline(0;0)(5.196;300)}
\rput(-6.062,-4.5){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;300)}
\rput(3.464,0){\psline(0;0)(5.196;300)}
\rput(5.196,0){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;120)}
\rput(3.464,0){\psline(0;0)(6.928;120)}
\rput(5.196,0){\psline(0;0)(6.928;120)}
\rput(6.062,1.5){\psline(0;0)(5.196;120)}
\rput(6.062,4.5){\psline(0;0)(1.732;120)}

\rput(0,1){\psline(0;0)(7;150)}
\rput(0,1){\psline(0;0)(7;330)}
\rput(0,2){\psline(0;0)(7;150)}
\rput(0,2){\psline(0;0)(7;330)}
\rput(0,3){\psline(0;0)(6;150)}
\rput(0,3){\psline(0;0)(7;330)}
\rput(0,4){\psline(0;0)(4;150)}
\rput(0,4){\psline(0;0)(7;330)}
\rput(0,5){\psline(0;0)(7;330)}
\rput(0,6){\psline(0;0)(7;330)}
\rput(-1.732,6){\psline(0;0)(2;330)}

\rput(0,-1){\psline(0;0)(7;150)}
\rput(0,-1){\psline(0;0)(7;330)}
\rput(0,-2){\psline(0;0)(7;150)}
\rput(0,-2){\psline(0;0)(7;330)}
\rput(0,-3){\psline(0;0)(7;150)}
\rput(0,-3){\psline(0;0)(6;330)}
\rput(0,-4){\psline(0;0)(7;150)}
\rput(0,-4){\psline(0;0)(4;330)}
\rput(0,-5){\psline(0;0)(7;150)}
\rput(0,-5){\psline(0;0)(2;330)}
\rput(0,-6){\psline(0;0)(7;150)}

\rput(6.062,3.5){\psline(0;0)(5;150)}
\rput(6.062,4.5){\psline(0;0)(3;150)}
\rput(6.062,5.5){\psline(0;0)(1;150)}

\rput(-6.062,-3.5){\psline(0;0)(5;330)}
\rput(-6.062,-4.5){\psline(0;0)(3;330)}
\rput(-6.062,-5.5){\psline(0;0)(1;330)}

\psline(0;0)(7;330)
\psline(0;0)(7;150)
\psline(0;0)(7;210)
\psline(0;0)(6.928;240)

\pspolygon[fillcolor=gray,fillstyle=solid](0,0)(0,1)(0.433,0.75)

\psline[linewidth=1mm](0,1)(0,1.5)
\psline[linewidth=1mm](0,1)(.433,.75)
\psline[linewidth=1mm](0,0)(.866,1.5)
\psline[linewidth=1mm](.866,1.5)(0,1.5)
\psline[linewidth=1mm](-.866,1.5)(0,1)
\psline[linewidth=1mm](0,1)(0,0)
\psline[linewidth=1mm](0,0)(-.866,1.5)

\psline[linewidth=1mm](0,1.5)(0,3)
\psline[linewidth=1mm](0,3)(-1.732,6)
\psline[linewidth=1mm](-.866,1.5)(-3.464,6)

\psline[linewidth=1mm](.433,.75)(1.732,0)
\psline[linewidth=1mm](1.732,0)(6.062,0)
\psline[linewidth=1mm](2.598,1.5)(6.062,1.5)

\psline[linewidth=1mm](-.433,.75)(-1.732,0)
\psline[linewidth=1mm](-1.732,0)(-6.062,0)
\psline[linewidth=1mm](-2.598,1.5)(-6.062,1.5)

\psline[linewidth=1mm](.866,0)(.866,-1.5)
\psline[linewidth=1mm](.866,-1.5)(3.464,-6)
\psline[linewidth=1mm](.866,0)(1.732,0)
\psline[linewidth=1mm](2.598,-1.5)(5.196,-6)

\psline[linewidth=1mm](-.866,0)(-.866,-1.5)
\psline[linewidth=1mm](-.866,-1.5)(-3.464,-6)
\psline[linewidth=1mm](-.866,0)(-1.732,0)
\psline[linewidth=1mm](-2.598,-1.5)(-5.196,-6)

\psline[linewidth=1mm](.433,2.25)(0,3)
\psline[linewidth=1mm](0.866,4.5)(1.732,6)
\psline[linewidth=1mm](.433,2.25)(1.732,3)
\psline[linewidth=1mm](1.732,3)(3.464,6)

\psline[linewidth=1mm](0,0)(0,-6)
\psline[linewidth=1mm](0,0)(.866,-1.5)
\psline[linewidth=1mm](.866,-1.5)(.866,-6)

\psline[linewidth=1mm](1.732,0)(6.062,-2.5)
\psline[linewidth=1mm](2.598,-1.5)(6.062,-3.5)

\psline[linewidth=1mm](-1.732,0)(-6.062,-2.5)
\psline[linewidth=1mm](-2.598,-1.5)(-6.062,-3.5)

\psline[linewidth=1mm](.866,1.5)(6.062,4.5)
\psline[linewidth=1mm](2.598,1.5)(6.062,3.5)

\psline[linewidth=1mm](-.866,1.5)(-6.062,4.5)
\psline[linewidth=1mm](-2.598,1.5)(-6.062,3.5)

\psline[linewidth=1mm](0,3)(0,6)
\psline[linewidth=1mm](.866,4.5)(.866,6)

\psline[linewidth=1mm](.866,1.5)(1.732,3)
\psline[linewidth=1mm](0,0)(-.866,-1.5)

\psline[linewidth=1mm](-.866,.5)(-2.598,1.5)
\psline[linewidth=1mm](.866,.5)(2.598,1.5)
\psline[linewidth=1mm](.866,2.5)(.866,4.5)
\psline[linewidth=1mm](.866,-.5)(2.598,-1.5)
\psline[linewidth=1mm](-.866,-.5)(-2.598,-1.5)

\psline[linewidth=1mm](1.732,0)(2.598,-1.5)
\psline[linewidth=1mm](.866,1.5)(2.598,1.5)
\psline[linewidth=1mm](-.866,1.5)(-2.598,1.5)
\psline[linewidth=1mm](-1.732,0)(-2.598,-1.5)
\psline[linewidth=1mm](0,3)(.866,4.5)

\rput(0,-7){\textsc{Figure 6}. Partition of $\tilde{G}_{2}$ into cells}

\rput(-1.5,-4.33){{\small ${\bf \tilde{c}_{0}^{1}}$}}
\rput(1.988,-4.31){{\small ${\bf \tilde{c}_{0}^{2}}$}}
\rput(5.452,-4.31){{\small ${\bf \tilde{c}_{0}^{3}}$}}
\rput(5.452,-1.31){{\small ${\bf \tilde{c}_{0}^{4}}$}}
\rput(3.69,1.7){{\small ${\bf \tilde{c}_{0}^{5}}$}}
\rput(2.824,3.2){{\small ${\bf \tilde{c}_{0}^{6}}$}}
\rput(1.1,5.75){{\small ${\bf \tilde{c}_{0}^{7}}$}}
\rput(-0.23,4.67){{\small ${\bf \tilde{c}_{0}^{8}}$}}
\rput(-2.372,3.2){{\small ${\bf \tilde{c}_{0}^{9}}$}}
\rput(-4.97,1.7){{\small ${\bf \tilde{c}_{0}^{10}}$}}

\rput(-4.97,-1.3){{\small ${\bf \tilde{c}_{0}^{11}}$}}
\rput(-4.97,-4.3){{\small ${\bf \tilde{c}_{0}^{12}}$}}

\rput(2.3,-2.33){{\small ${\bf  \tilde{c}_{2}^{1}}$}}
\rput(3.2,.73){{\small ${\bf \tilde{c}_{2}^{2}}$}}
\rput(1.5,4.34){{\small ${\bf \tilde{c}_{2}^{3}}$}}
\rput(-1.5,4.34){{\small ${\bf \tilde{c}_{2}^{4}}$}}
\rput(-3.2,.73){{\small ${\bf \tilde{c}_{2}^{5}}$}}
\rput(-2.3,-2.33){{\small ${\bf  \tilde{c}_{2}^{6}}$}}

\rput(0.3,-4.33){{\small ${\bf  \tilde{c}_{1}^{1}}$}}
\rput(3.2,-1.33){{\small ${\bf \tilde{c}_{1}^{2}}$}}
\rput(3.2,2.34){{\small ${\bf \tilde{c}_{1}^{3}}$}}
\rput(0.3,4.33){{\small ${\bf \tilde{c}_{1}^{4}}$}}
\rput(-3.4,2.34){{\small ${\bf \tilde{c}_{1}^{5}}$}}
\rput(-3.2,-1.33){{\small ${\bf \tilde{c}_{1}^{6}}$}}

\rput(1.3,-.37){{\small ${\bf \tilde{c}_{3}^{1}}$}}
\rput(1.3,1.07){{\small ${\bf \tilde{c}_{3}^{2}}$}}
\rput(.59,3.2){{\small ${\bf \tilde{c}_{3}^{3}}$}}
\rput(-1.3,1.07){{\small ${\bf \tilde{c}_{3}^{4}}$}}
\rput(-1.3,-.46){{\small ${\bf \tilde{c}_{3}^{5}}$}}

\rput(.6,.19){{\small ${\bf \tilde{c}_{4}^{1}}$}}
\rput(.4,1.93){{\small ${\bf \tilde{c}_{4}^{2}}$}}
\rput(-.49,.23){{\small ${\bf \tilde{c}_{4}^{3}}$}}

\rput(.3,1.1){{\small ${\bf \tilde{c}_{5}^{1}}$}}
\rput(-.23,.73){{\small ${\bf \tilde{c}_{5}^{2}}$}}

\rput(.17,.68){{\small ${\bf \tilde{c}_{6}^{1}}$}}

\end{pspicture}
\end{center}

\newpage

\begin{center}
\begin{pspicture}(-1.3,-1.5)(13,13)
\psset{unit=.7pt}

\pscircle(-100,0){10}
\rput(-100,0){{\small $u_{0}^{1}$}}
\pscircle(-60,0){10}
\rput(-60,0){{\small $u_{0}^{2}$}}

\pscircle(0,0){10}
\rput(0,0){{\small $u_{0}^{3}$}}
\pscircle(40,0){10}
\rput(40,0){{\small $u_{0}^{4}$}}
\pscircle(100,0){10}
\rput(100,0){{\small $u_{0}^{5}$}}
\pscircle(140,0){10}
\rput(140,0){{\small $u_{0}^{6}$}}

\pscircle(200,0){10}
\rput(200,0){{\small $u_{0}^{7}$}}
\pscircle(240,0){10}
\rput(240,0){{\small $u_{0}^{8}$}}

\pscircle(300,0){10}
\rput(300,0){{\small $u_{0}^{9}$}}
\pscircle(340,0){10}
\rput(340,0){{\small $u_{0}^{10}$}}

\pscircle(400,0){10}
\rput(400,0){{\small $u_{0}^{11}$}}
\pscircle(440,0){10}
\rput(440,0){{\small $u_{0}^{12}$}}

\pscircle(500,0){10}
\rput(500,0){{\small $u_{0}^{1}$}}
\pscircle(540,0){10}
\rput(540,0){{\small $u_{0}^{2}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](-80,150){10}
\rput(-80,150){{\scriptsize $u_{1}^{1}$}}

\pscircle(0,150){10}
\rput(0,150){{\scriptsize $u_{1}^{2}$}}

\pscircle(40,150){10}
\rput(40,150){{\scriptsize $u_{2}^{1}$}}

\pscircle(100,150){10}
\rput(100,150){{\scriptsize $u_{1}^{3}$}}

\pscircle(140,150){10}
\rput(140,150){{\scriptsize $u_{2}^{2}$}}

\pscircle(200,150){10}
\rput(200,150){{\scriptsize $u_{1}^{4}$}}

\pscircle(240,150){10}
\rput(240,150){{\scriptsize $u_{2}^{3}$}}

\pscircle(300,150){10}
\rput(300,150){{\scriptsize $u_{1}^{5}$}}

\pscircle(340,150){10}
\rput(340,150){{\scriptsize $u_{2}^{5}$}}

\pscircle(400,150){10}
\rput(400,150){{\scriptsize $u_{1}^{6}$}}

\pscircle(440,150){10}
\rput(440,150){{\scriptsize $u_{2}^{6}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](270,150){10}
\rput(270,150){{\scriptsize $u_{2}^{4}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](520,150){10}
\rput(520,150){{\scriptsize $u_{1}^{1}$}}

\pscircle(-80,93){3}

\pscircle(20,93){3}

\pscircle(120,93){3}

\pscircle(220,93){3}

\pscircle(320,93){3}

\pscircle(420,93){3}

\pscircle(520,93){3}

\pscircle(20,200){10}
\rput(20,200){{\scriptsize$u_{3}^{1}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](120,200){10}
\rput(120,200){{\scriptsize$u_{3}^{2}$}}

\pscircle(220,200){10}
\rput(220,200){{\scriptsize$u_{3}^{3}$}}

\pscircle(320,200){10}
\rput(320,200){{\scriptsize$u_{3}^{4}$}}

\pscircle(420,200){10}
\rput(420,200){{\scriptsize$u_{3}^{5}$}}

\pscircle(70,300){10}
\rput(70,300){{\tiny $u_{4}^{1}$}}

\pscircle(245,300){10}
\rput(245,300){{\tiny $u_{4}^{2}$}}

\pscircle(370,300){10}
\rput(370,300){{\tiny $u_{4}^{3}$}}

\pscircle(307.5,350){3}

\pscircle(280,400){10}
\rput(280,400){{\scriptsize$u_{5}^{1}$}}

\pscircle(335,400){10}
\rput(335,400){{\scriptsize$u_{5}^{2}$}}

\pscircle(307.5,450){10}
\rput(307.5,450){{\scriptsize$u_{6}^{2}$}}

\psline(-80,90)(-100,10)
\psline(-80,90)(-60,10)

\psline(20,90)(0,10)
\psline(20,90)(40,10)

\psline(20,90)(-100,10)

\psline(20,90)(-60,10)

\psline(20,90)(140,10)

\psline(120,90)(100,10)
\psline(120,90)(140,10)

\psline(120,90)(40,10)

\psline(220,90)(200,10)
\psline(220,90)(240,10)

\psline(220,90)(300,10)

\psline(320,90)(300,10)
\psline(320,90)(340,10)

\psline(320,90)(400,10)

\psline(420,90)(400,10)
\psline(420,90)(440,10)

\psline(420,90)(300,10)

\psline(520,90)(500,10)
\psline(520,90)(540,10)

\psline(220,90)(40,10)

\psline(220,90)(140,10)

\psline(320,90)(500,10)

\psline(420,90)(500,10)

\psline(-80,140)(-80,96)

\psline(0,140)(20,96)
\psline(40,140)(20,96)

\psline(100,140)(120,96)
\psline(140,140)(120,96)

\psline(200,140)(220,96)
\psline(240,140)(220,96)

\psline(300,140)(320,96)
\psline(340,140)(320,96)

\psline(400,140)(420,96)
\psline(440,140)(420,96)

\psline(520,140)(520,96)

\psline(270,140)(200,10)

\psline(270,140)(300,10)

\psline(20,190)(0,160)
\psline(20,190)(40,160)

\psline(120,190)(100,160)
\psline(120,190)(140,160)

\psline(220,190)(200,160)
\psline(220,190)(240,160)

\psline(320,190)(300,160)
\psline(320,190)(340,160)

\psline(420,190)(400,160)
\psline(420,190)(440,160)

\psline(70,290)(-80,160)

\psline(70,290)(20,210)

\psline(70,290)(120,210)

\psline(245,290)(120,210)

\psline(245,290)(220,210)

\psline(245,290)(270,160)

\psline(370,290)(320,210)

\psline(370,290)(420,210)

\psline(280,390)(307.5,353)
\psline(307.5,347)(270,160)
\psline(335,390)(307.5,353)

\psline(280,390)(245,310)

\psline(335,390)(370,310)

\psline(307.5,440)(280,410)

\psline(307.5,440)(335,410)

\psline(307.5,440)(70,310)

\rput(250,-50){Figure 7. Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\vspace{2cm}

Let $w=s_{1}s_{2}s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3}$ and $w_{1}=s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}$. In the following table we have
$$y\in \{zw^{n}| z\in Y(w), n\in\mathbb{N}\} \text{ and } y_{1}\in \{yw_{1}^{n}| y\in Y(w_{1}), n\in\mathbb{N}\} $$

\newpage

{\footnotesize
\begin{table}[htbp] \caption{Condition {\bf I5} $3/2<r<2$}
\label{PcG}
\begin{textblock}{21}(0,4)
\renewcommand{\arraystretch}{1.3}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{1}^{2} & ys_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+2b} T_{y}C_{u_{0}^{1}}\\\hline

u_{1}^{4} & s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b} C_{u_{0}^{6}}-v^{-a+2b}C_{u_{0}^{9}}\\\hline
u_{1}^{4} & s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b} T_{s_{3}}C_{u_{0}^{6}}-v^{-a+2b}T_{s_{3}}C_{u_{0}^{9}}\\\hline
u_{1}^{4} & s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} &
T_{xu} +v^{-a+3b} T_{s_{2}s_{3}}C_{u_{0}^{6}}-v^{-a+2b}T_{s_{2}s_{3}}C_{u_{0}^{9}}\\\hline
u_{1}^{4} & s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} &
T_{xu} +v^{-a+3b} T_{s_{1}s_{2}s_{3}}C_{u_{0}^{6}}-v^{-a+2b}T_{s_{1}s_{2}s_{3}}C_{u_{0}^{9}}\\\hline
u_{1}^{4} & s_{2}s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} &
T_{xu} +v^{-a+3b} T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}-v^{-a+2b}T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{9}}\\\hline
u_{1}^{4} & yw&
T_{xu} +v^{-a+3b} T_{ys_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}-v^{-a+2b} T_{ys_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}-v^{-a+2b}T_{ys_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{9}}\\\hline

u_{1}^{6} & s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{-a+3b} C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b} T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b} T_{s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b} T_{s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{1}s_{2}s_{3}s_{1}s_{2}s_{1}s_{2}s_{3} & T_{xu} +v^{-a+3b} T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & yw &
T_{xu} +v^{-a+3b} T_{ys_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}-v^{a-2b}T_{ys_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{1} & s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{a-b} C_{u_{0}^{1}}\\\hline
u_{2}^{1} &  s_{3}s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{a-b} T_{s_{2}}C_{u_{0}^{1}}\\\hline
u_{2}^{1} & y_{1}w_{1}& T_{xu} +v^{a-b} T_{y_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{1} & y_{1}w_{1}s_{3}s_{2}s_{1} & T_{xu} +v^{a-b} T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{3} & s_{1}s_{2}s_{1} & T_{xu} -v^{a-b} C_{u_{0}^{6}}\\\hline
u_{2}^{3} & s_{2}s_{1}s_{2}s_{1} & T_{xu} -v^{a} C_{u_{0}^{6}}\\\hline
u_{2}^{3} & s_{3}s_{2}s_{1}s_{2}s_{1} & T_{xu} -v^{a} C_{s_{3}u_{0}^{6}}\\\hline

u_{2}^{3} & y_{1}w_{1} & T_{xu} -v^{a}T_{y_{1}s_{3}} C_{u_{0}^{6}}+T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline

u_{2}^{3} & s_{3}s_{2}s_{1} & T_{xu} -v^{a-b} T_{s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{3} & s_{1}s_{3}s_{2}s_{1} & T_{xu} -v^{a-b} T_{s_{3}}C_{u_{0}^{6}}+T_{s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline

u_{2}^{3} & s_{2}s_{1}s_{3}s_{2}s_{1} & T_{xu} +v^{a+b} T_{s_{2}s_{3}}C_{u_{0}^{6}}+T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{3} & s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +v^{a+b} T_{s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+T_{s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{3} & s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +v^{a+b} T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+T_{s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{3} & s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +v^{a+b} T_{s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+T_{s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{3} & y_{1}w_{1}s_{3}s_{2}s_{1} &
T_{xu} +v^{a} T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline

u_{2}^{6} & s_{1}s_{2}s_{1} & T_{xu} +v^{a+b} C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{a} C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{3}s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{a} C_{s_{3}u_{0}^{1}}\\\hline
u_{2}^{6} & y_{1}w_{1} & T_{xu} +v^{a}T_{y_{1}s_{3}} C_{u_{0}^{1}}+T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{6} & s_{3}s_{2}s_{1} & T_{xu} +v^{a+b} T_{s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{1}s_{3}s_{2}s_{1} & T_{xu} +v^{a+b} T_{s_{3}}C_{u_{0}^{1}}+T_{s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{6} & s_{2}s_{1}s_{3}s_{2}s_{1} & T_{xu} +v^{a+b} T_{s_{2}s_{3}}C_{u_{0}^{1}}+T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +v^{a+b} T_{s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+T_{s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +v^{a+b} T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+T_{s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +v^{a+b} T_{s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+T_{s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & y_{1}w_{1}s_{3}s_{2}s_{1} &
T_{xu} +v^{a} T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{3}^{3} & s_{2}s_{1}s_{2} & T_{xu}+C_{u_{0}^{6}}\\\hline
u_{3}^{3} & s_{3}s_{2}s_{1}s_{2} & T_{xu}+T_{s_{3}}C_{u_{0}^{6}}\\\hline

u_{3}^{5} & s_{2}s_{1}s_{2} & T_{xu}+C_{u_{0}^{1}}\\\hline
u_{3}^{5} & s_{3}s_{2}s_{1}s_{2} & T_{xu}+T_{s_{3}}C_{u_{0}^{1}}\\\hline

 \end{array}$
 \end{textblock}
\end{table}}

\newpage

\item {\bf Case ${\bf r=3/2}$}

\begin{center}
\begin{pspicture}(-6,-6)(6,9)
\psset{unit=1.3cm}

\SpecialCoor
\psline(0,-6)(0,6)
\multido{\n=1+1}{7}{
\psline(\n;30)(\n;330)}
\rput(1;30){\psline(0,0)(0,5.5)}
\rput(1;330){\psline(0,0)(0,-5.5)}
\rput(2;30){\psline(0,0)(0,5)}
\rput(2;330){\psline(0,0)(0,-5)}
\rput(3;30){\psline(0,0)(0,4.5)}
\rput(3;330){\psline(0,0)(0,-4.5)}
\rput(4;30){\psline(0,0)(0,4)}
\rput(4;330){\psline(0,0)(0,-4)}
\rput(5;30){\psline(0,0)(0,3.5)}
\rput(5;330){\psline(0,0)(0,-3.5)}
\rput(6;30){\psline(0,0)(0,3)}
\rput(6;330){\psline(0,0)(0,-3)}
\rput(7;30){\psline(0,0)(0,2.5)}
\rput(7;330){\psline(0,0)(0,-2.5)}
\multido{\n=1+1}{7}{
\psline(\n;150)(\n;210)}
\rput(1;150){\psline(0,0)(0,5.5)}
\rput(1;210){\psline(0,0)(0,-5.5)}
\rput(2;150){\psline(0,0)(0,5)}
\rput(2;210){\psline(0,0)(0,-5)}
\rput(3;150){\psline(0,0)(0,4.5)}
\rput(3;210){\psline(0,0)(0,-4.5)}
\rput(4;150){\psline(0,0)(0,4)}
\rput(4;210){\psline(0,0)(0,-4)}
\rput(5;150){\psline(0,0)(0,3.5)}
\rput(5;210){\psline(0,0)(0,-3.5)}
\rput(6;150){\psline(0,0)(0,3)}
\rput(6;210){\psline(0,0)(0,-3)}
\rput(7;150){\psline(0,0)(0,2.5)}
\rput(7;210){\psline(0,0)(0,-2.5)}
\multido{\n=1.5+1.5}{4}{
\psline(-6.062,\n)(6.062,\n)}
\multido{\n=0+1.5}{5}{
\psline(-6.062,-\n)(6.062,-\n)}
\psline(0;0)(7;30)

\rput(0,1){\psline(0;0)(7;30)}
\rput(0,1){\psline(0;0)(7;210)}
\rput(0,2){\psline(0;0)(7;30)}
\rput(0,2){\psline(0;0)(7;210)}
\rput(0,3){\psline(0;0)(6;30)}
\rput(0,3){\psline(0;0)(7;210)}
\rput(0,4){\psline(0;0)(4;30)}
\rput(0,4){\psline(0;0)(7;210)}
\rput(0,5){\psline(0;0)(2;30)}
\rput(0,5){\psline(0;0)(7;210)}
\rput(0,6){\psline(0;0)(7;210)}
\rput(-1.732,6){\psline(0;0)(5;210)}
\rput(-3.464,6){\psline(0;0)(3;210)}
\rput(-5.196,6){\psline(0;0)(1;210)}

\rput(0,-1){\psline(0;0)(7;30)}
\rput(0,-1){\psline(0;0)(7;210)}
\rput(0,-2){\psline(0;0)(7;30)}
\rput(0,-2){\psline(0;0)(7;210)}
\rput(0,-3){\psline(0;0)(7;30)}
\rput(0,-3){\psline(0;0)(6;210)}
\rput(0,-4){\psline(0;0)(7;30)}
\rput(0,-4){\psline(0;0)(4;210)}
\rput(0,-5){\psline(0;0)(7;30)}
\rput(0,-5){\psline(0;0)(2;210)}
\rput(0,-6){\psline(0;0)(7;30)}
\rput(1.732,-6){\psline(0;0)(5;30)}
\rput(3.464,-6){\psline(0;0)(3;30)}
\rput(5.196,-6){\psline(0;0)(1;30)}

\psline(0;0)(6.928;60)
\rput(1.732,0){\psline(0;0)(6.928;60)}
\rput(3.464,0){\psline(0;0)(5.196;60)}
\rput(5.196,0){\psline(0;0)(1.732;60)}
\rput(1.732,0){\psline(0;0)(6.928;240)}
\rput(3.464,0){\psline(0;0)(6.928;240)}
\rput(5.196,0){\psline(0;0)(6.928;240)}
\rput(6.062,-1.5){\psline(0;0)(5.196;240)}
\rput(6.062,-4.5){\psline(0;0)(1.732;240)}
\rput(-1.732,0){\psline(0;0)(6.928;60)}
\rput(-3.464,0){\psline(0;0)(6.928;60)}
\rput(-5.196,0){\psline(0;0)(6.928;60)}
\rput(-1.732,0){\psline(0;0)(6.928;240)}
\rput(-3.464,0){\psline(0;0)(5.196;240)}
\rput(-5.196,0){\psline(0;0)(1.732;240)}
\rput(-6.062,1.5){\psline(0;0)(5.196;60)}
\rput(-6.062,4.5){\psline(0;0)(1.732;60)}

\psline(0;0)(6.928;120)
\psline(0;0)(6.928;300)
\rput(-1.732,0){\psline(0;0)(6.928;120)}
\rput(-3.464,0){\psline(0;0)(5.196;120)}
\rput(-5.196,0){\psline(0;0)(1.732;120)}
\rput(-1.732,0){\psline(0;0)(6.928;300)}
\rput(-3.464,0){\psline(0;0)(6.928;300)}
\rput(-5.196,0){\psline(0;0)(6.928;300)}
\rput(-6.062,-1.5){\psline(0;0)(5.196;300)}
\rput(-6.062,-4.5){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;300)}
\rput(3.464,0){\psline(0;0)(5.196;300)}
\rput(5.196,0){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;120)}
\rput(3.464,0){\psline(0;0)(6.928;120)}
\rput(5.196,0){\psline(0;0)(6.928;120)}
\rput(6.062,1.5){\psline(0;0)(5.196;120)}
\rput(6.062,4.5){\psline(0;0)(1.732;120)}

\rput(0,1){\psline(0;0)(7;150)}
\rput(0,1){\psline(0;0)(7;330)}
\rput(0,2){\psline(0;0)(7;150)}
\rput(0,2){\psline(0;0)(7;330)}
\rput(0,3){\psline(0;0)(6;150)}
\rput(0,3){\psline(0;0)(7;330)}
\rput(0,4){\psline(0;0)(4;150)}
\rput(0,4){\psline(0;0)(7;330)}
\rput(0,5){\psline(0;0)(7;330)}
\rput(0,6){\psline(0;0)(7;330)}
\rput(-1.732,6){\psline(0;0)(2;330)}

\rput(0,-1){\psline(0;0)(7;150)}
\rput(0,-1){\psline(0;0)(7;330)}
\rput(0,-2){\psline(0;0)(7;150)}
\rput(0,-2){\psline(0;0)(7;330)}
\rput(0,-3){\psline(0;0)(7;150)}
\rput(0,-3){\psline(0;0)(6;330)}
\rput(0,-4){\psline(0;0)(7;150)}
\rput(0,-4){\psline(0;0)(4;330)}
\rput(0,-5){\psline(0;0)(7;150)}
\rput(0,-5){\psline(0;0)(2;330)}
\rput(0,-6){\psline(0;0)(7;150)}

\rput(6.062,3.5){\psline(0;0)(5;150)}
\rput(6.062,4.5){\psline(0;0)(3;150)}
\rput(6.062,5.5){\psline(0;0)(1;150)}

\rput(-6.062,-3.5){\psline(0;0)(5;330)}
\rput(-6.062,-4.5){\psline(0;0)(3;330)}
\rput(-6.062,-5.5){\psline(0;0)(1;330)}

\psline(0;0)(7;330)
\psline(0;0)(7;150)
\psline(0;0)(7;210)
\psline(0;0)(6.928;240)

\pspolygon[fillcolor=gray,fillstyle=solid](0,0)(0,1)(0.433,0.75)

\psline[linewidth=1mm](0,1)(0,1.5)
\psline[linewidth=1mm](0,1)(.433,.75)
\psline[linewidth=1mm](0,0)(.866,1.5)
\psline[linewidth=1mm](.866,1.5)(0,1.5)
\psline[linewidth=1mm](-.866,1.5)(0,1)
\psline[linewidth=1mm](0,1)(0,0)
\psline[linewidth=1mm](0,0)(-.866,1.5)

\psline[linewidth=1mm](0,1.5)(0,3)
\psline[linewidth=1mm](0,3)(-1.732,6)
\psline[linewidth=1mm](-.866,1.5)(-3.464,6)

\psline[linewidth=1mm](.433,.75)(1.732,0)
\psline[linewidth=1mm](1.732,0)(6.062,0)
\psline[linewidth=1mm](2.598,1.5)(6.062,1.5)

\psline[linewidth=1mm](-.433,.75)(-1.732,0)
\psline[linewidth=1mm](-1.732,0)(-6.062,0)
\psline[linewidth=1mm](-2.598,1.5)(-6.062,1.5)

\psline[linewidth=1mm](.866,0)(.866,-1.5)
\psline[linewidth=1mm](.866,-1.5)(3.464,-6)
\psline[linewidth=1mm](.866,0)(1.732,0)
\psline[linewidth=1mm](2.598,-1.5)(5.196,-6)

\psline[linewidth=1mm](-.866,0)(-.866,-1.5)
\psline[linewidth=1mm](-.866,-1.5)(-3.464,-6)
\psline[linewidth=1mm](-.866,0)(-1.732,0)
\psline[linewidth=1mm](-2.598,-1.5)(-5.196,-6)

\psline[linewidth=1mm](.433,2.25)(0,3)
\psline[linewidth=1mm](0.866,4.5)(1.732,6)
\psline[linewidth=1mm](.433,2.25)(1.732,3)
\psline[linewidth=1mm](1.732,3)(3.464,6)

\psline[linewidth=1mm](0,0)(0,-6)
\psline[linewidth=1mm](0,0)(.866,-1.5)
\psline[linewidth=1mm](.866,-1.5)(.866,-6)

\psline[linewidth=1mm](1.732,0)(6.062,-2.5)
\psline[linewidth=1mm](2.598,-1.5)(6.062,-3.5)

\psline[linewidth=1mm](-1.732,0)(-6.062,-2.5)
\psline[linewidth=1mm](-2.598,-1.5)(-6.062,-3.5)

\psline[linewidth=1mm](.866,1.5)(6.062,4.5)
\psline[linewidth=1mm](2.598,1.5)(6.062,3.5)

\psline[linewidth=1mm](-.866,1.5)(-6.062,4.5)
\psline[linewidth=1mm](-2.598,1.5)(-6.062,3.5)

\psline[linewidth=1mm](0,3)(0,6)
\psline[linewidth=1mm](.866,4.5)(.866,6)

\psline[linewidth=1mm](.866,1.5)(1.732,3)
\psline[linewidth=1mm](0,0)(-.866,-1.5)

\psline[linewidth=1mm](-.866,.5)(-2.598,1.5)
\psline[linewidth=1mm](.866,.5)(2.598,1.5)
\psline[linewidth=1mm](.866,2.5)(.866,4.5)
\psline[linewidth=1mm](.866,-.5)(2.598,-1.5)
\psline[linewidth=1mm](-.866,-.5)(-2.598,-1.5)

\rput(0,-7){\textsc{Figure 8}. Partition of $\tilde{G}_{2}$ into cells}

\rput(-1.5,-4.33){{\small ${\bf \tilde{c}_{0}^{1}}$}}
\rput(1.988,-4.31){{\small ${\bf \tilde{c}_{0}^{2}}$}}
\rput(5.452,-4.31){{\small ${\bf \tilde{c}_{0}^{3}}$}}
\rput(5.452,-1.31){{\small ${\bf \tilde{c}_{0}^{4}}$}}
\rput(3.69,1.7){{\small ${\bf \tilde{c}_{0}^{5}}$}}
\rput(2.824,3.2){{\small ${\bf \tilde{c}_{0}^{6}}$}}
\rput(1.1,5.75){{\small ${\bf \tilde{c}_{0}^{7}}$}}
\rput(-0.23,4.67){{\small ${\bf \tilde{c}_{0}^{8}}$}}
\rput(-2.372,3.2){{\small ${\bf \tilde{c}_{0}^{9}}$}}
\rput(-4.97,1.7){{\small ${\bf \tilde{c}_{0}^{10}}$}}

\rput(-4.97,-1.3){{\small ${\bf \tilde{c}_{0}^{11}}$}}
\rput(-4.97,-4.3){{\small ${\bf \tilde{c}_{0}^{12}}$}}

\rput(2.3,-2.33){{\small ${\bf  \tilde{c}_{1}^{1}}$}}
\rput(3.2,.73){{\small ${\bf \tilde{c}_{1}^{2}}$}}
\rput(1.5,4.34){{\small ${\bf \tilde{c}_{1}^{3}}$}}
\rput(-1.5,4.34){{\small ${\bf \tilde{c}_{1}^{4}}$}}
\rput(-3.2,.73){{\small ${\bf \tilde{c}_{1}^{5}}$}}
\rput(-2.3,-2.33){{\small ${\bf  \tilde{c}_{1}^{6}}$}}

\rput(0.3,-4.33){{\small ${\bf  \tilde{c}_{2}^{1}}$}}
\rput(3.2,-1.33){{\small ${\bf \tilde{c}_{2}^{2}}$}}
\rput(3.2,2.34){{\small ${\bf \tilde{c}_{2}^{3}}$}}
\rput(0.3,4.33){{\small ${\bf \tilde{c}_{2}^{4}}$}}
\rput(-3.4,2.34){{\small ${\bf \tilde{c}_{2}^{5}}$}}
\rput(-3.2,-1.33){{\small ${\bf \tilde{c}_{2}^{6}}$}}

\rput(.6,.19){{\small ${\bf \tilde{c}_{4}^{1}}$}}
\rput(.4,1.93){{\small ${\bf \tilde{c}_{4}^{2}}$}}
\rput(-.49,.23){{\small ${\bf \tilde{c}_{4}^{3}}$}}

\rput(.3,1.1){{\small ${\bf \tilde{c}_{5}^{1}}$}}
\rput(-.23,.73){{\small ${\bf \tilde{c}_{5}^{2}}$}}

\rput(.17,.68){{\small ${\bf \tilde{c}_{6}^{1}}$}}

\end{pspicture}
\end{center}

\newpage

\begin{center}

\begin{pspicture}(-1.3,-1.5)(13,13)
\psset{unit=.7pt}

\pscircle(-100,0){10}
\rput(-100,0){{\small $u_{0}^{1}$}}
\pscircle(-60,0){10}
\rput(-60,0){{\small $u_{0}^{2}$}}

\pscircle(0,0){10}
\rput(0,0){{\small $u_{0}^{3}$}}
\pscircle(40,0){10}
\rput(40,0){{\small $u_{0}^{4}$}}
\pscircle(100,0){10}
\rput(100,0){{\small $u_{0}^{5}$}}
\pscircle(140,0){10}
\rput(140,0){{\small $u_{0}^{6}$}}

\pscircle(200,0){10}
\rput(200,0){{\small $u_{0}^{7}$}}
\pscircle(240,0){10}
\rput(240,0){{\small $u_{0}^{8}$}}

\pscircle(300,0){10}
\rput(300,0){{\small $u_{0}^{9}$}}
\pscircle(340,0){10}
\rput(340,0){{\small $u_{0}^{10}$}}

\pscircle(400,0){10}
\rput(400,0){{\small $u_{0}^{11}$}}
\pscircle(440,0){10}
\rput(440,0){{\small $u_{0}^{12}$}}

\pscircle(500,0){10}
\rput(500,0){{\small $u_{0}^{1}$}}
\pscircle(540,0){10}
\rput(540,0){{\small $u_{0}^{2}$}}

\pscircle(20,100){10}
\rput(20,100){{\scriptsize $u_{1}^{1}$}}

\pscircle(120,100){10}
\rput(120,100){{\scriptsize $u_{1}^{2}$}}

\pscircle(220,100){10}
\rput(220,100){{\scriptsize $u_{1}^{3}$}}

\pscircle(270,100){10}
\rput(270,100){{\scriptsize $u_{1}^{4}$}}

\pscircle(320,100){10}
\rput(320,100){{\scriptsize $u_{1}^{5}$}}

\pscircle(420,100){10}
\rput(420,100){{\scriptsize $u_{1}^{6}$}}

\pscircle(-80,200){10}
\rput(-80,200){{\scriptsize $u_{2}^{1}$}}

\pscircle(20,200){10}
\rput(20,200){{\scriptsize $u_{2}^{2}$}}

\pscircle(120,200){10}
\rput(120,200){{\scriptsize $u_{2}^{3}$}}

\pscircle(220,200){10}
\rput(220,200){{\scriptsize $u_{2}^{4}$}}

\pscircle(320,200){10}
\rput(320,200){{\scriptsize $u_{2}^{5}$}}

\pscircle(420,200){10}
\rput(420,200){{\scriptsize $u_{2}^{6}$}}

\pscircle(70,300){10}
\rput(70,300){{\tiny $u_{4}^{1}$}}

\pscircle(245,300){10}
\rput(245,300){{\tiny $u_{4}^{2}$}}

\pscircle(370,300){10}
\rput(370,300){{\tiny $u_{4}^{3}$}}

\pscircle(280,400){10}
\rput(280,400){{\scriptsize$u_{5}^{1}$}}

\pscircle(335,400){10}
\rput(335,400){{\scriptsize$u_{5}^{2}$}}

\pscircle(307.5,350){3}

\pscircle(307.5,450){10}
\rput(307.5,450){{\scriptsize$u_{6}^{1}$}}

\psline(20,90)(-60,10)

\psline(20,90)(40,10)

\psline(20,90)(-100,10)

\psline(20,90)(0,10)

\psline(20,90)(140,10)

\psline(120,90)(40,10)

\psline(120,90)(140,10)

\psline(120,90)(100,10)

\psline(220,90)(140,10)

\psline(220,90)(240,10)

\psline(220,90)(200,10)

\psline(220,90)(40,10)

\psline(220,90)(300,10)

\psline(270,90)(240,10)

\psline(270,90)(300,10)

\psline(320,90)(340,10)

\psline(320,90)(400,10)

\psline(320,90)(300,10)

\psline(320,90)(500,10)

\psline(420,90)(440,10)

\psline(420,90)(500,10)

\psline(420,90)(400,10)

\psline(420,90)(300,10)

\psline(-80,190)(-100,10)

\psline(-80,190)(-60,10)

\psline(20,190)(20,110)

\psline(120,190)(120,110)

\psline(220,190)(220,110)

\psline(320,190)(320,110)

\psline(420,190)(420,110)

\psline(70,290)(-80,210)

\psline(70,290)(20,210)

\psline(70,290)(120,210)

\psline(245,290)(120,210)

\psline(245,290)(220,210)

\psline(245,290)(270,110)

\psline(370,290)(320,210)

\psline(370,290)(420,210)

\psline(280,390)(245,310)

\psline(335,390)(370,310)

\psline(280,390)(307.5,353)
\psline(307.5,347)(270,110)
\psline(335,390)(307.5,353)

\psline(307.5,440)(280,410)

\psline(307.5,440)(335,410)

\psline(307.5,440)(70,310)
\rput(200,-50){Figure 9. Order $\preceq$ on $U$}

\end{pspicture}
\end{center}

\vspace{2cm}

Let $w=s_{1}s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1}s_{2}$, and $w_{1}=s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}$. In the following table we have
$$y\in \{zw^{n}| z\in Y(w), n\in\mathbb{N}\} \text{ and } y_{1}\in \{yw_{1}^{n}| y\in Y(w_{1}), n\in\mathbb{N}\} $$

 $\ $\\
{\small
\begin{table}[htbp] \caption{Condition {\bf I5} for $r=3/2$}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{1}^{1} & s_{2}s_{1}s_{2}s_{1} & T_{xu} +v C_{u_{0}^{1}}\\\hline
u_{1}^{1} & s_{3}s_{2}s_{1}s_{2}s_{1} & T_{xu} +v T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{1} & y_{1}w_{1} & T_{xu} +v T_{ys_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{1} & y_{1}w_{1}s_{3}s_{2}s_{1} & T_{xu}+vT_{ys_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{1}^{3} & s_{1}s_{2}s_{1} & T_{xu} +v C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{3} C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{3}s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{3} T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & y_{1}w_{1} & T_{xu} +v^{3} T_{ys_{3}}C_{u_{0}^{6}}+T_{ys_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+vT_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{2}s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+vT_{s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+vT_{s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+vT_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+vT_{s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & y_{1}w_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{ys_{2}s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+v^{3}T_{ys_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline

u_{1}^{6} & s_{1}s_{2}s_{1} & T_{xu} +v C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{3} C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{3}s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{3} T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & y_{1}w_{1} & T_{xu} +v^{3} T_{ys_{3}}C_{u_{0}^{1}}+T_{ys_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+vT_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+vT_{s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+vT_{s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+T_{s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & y_{1}w_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{y_{1}s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+v^{3}T_{ys_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{2} & s_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{2} & ys_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v T_{ys_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{4} & s_{2}s_{1}s_{2} & T_{xu} +C_{u_{0}^{6}}\\\hline
u_{2}^{4} & s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{4} & s_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{3}T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{4} & ys_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{3}T_{ys_{3}}C_{u_{0}^{6}}\\\hline

u_{2}^{6} & s_{2}s_{1}s_{2} & T_{xu} +C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{3}T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & ys_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{3}T_{ys_{3}}C_{u_{0}^{1}}\\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item {\bf Case ${\bf 1<r<3/2}$}
\begin{center}
\begin{pspicture}(-6,-6)(6,9)
\psset{unit=1.3cm}

\SpecialCoor
\psline(0,-6)(0,6)
\multido{\n=1+1}{7}{
\psline(\n;30)(\n;330)}
\rput(1;30){\psline(0,0)(0,5.5)}
\rput(1;330){\psline(0,0)(0,-5.5)}
\rput(2;30){\psline(0,0)(0,5)}
\rput(2;330){\psline(0,0)(0,-5)}
\rput(3;30){\psline(0,0)(0,4.5)}
\rput(3;330){\psline(0,0)(0,-4.5)}
\rput(4;30){\psline(0,0)(0,4)}
\rput(4;330){\psline(0,0)(0,-4)}
\rput(5;30){\psline(0,0)(0,3.5)}
\rput(5;330){\psline(0,0)(0,-3.5)}
\rput(6;30){\psline(0,0)(0,3)}
\rput(6;330){\psline(0,0)(0,-3)}
\rput(7;30){\psline(0,0)(0,2.5)}
\rput(7;330){\psline(0,0)(0,-2.5)}
\multido{\n=1+1}{7}{
\psline(\n;150)(\n;210)}
\rput(1;150){\psline(0,0)(0,5.5)}
\rput(1;210){\psline(0,0)(0,-5.5)}
\rput(2;150){\psline(0,0)(0,5)}
\rput(2;210){\psline(0,0)(0,-5)}
\rput(3;150){\psline(0,0)(0,4.5)}
\rput(3;210){\psline(0,0)(0,-4.5)}
\rput(4;150){\psline(0,0)(0,4)}
\rput(4;210){\psline(0,0)(0,-4)}
\rput(5;150){\psline(0,0)(0,3.5)}
\rput(5;210){\psline(0,0)(0,-3.5)}
\rput(6;150){\psline(0,0)(0,3)}
\rput(6;210){\psline(0,0)(0,-3)}
\rput(7;150){\psline(0,0)(0,2.5)}
\rput(7;210){\psline(0,0)(0,-2.5)}
\multido{\n=1.5+1.5}{4}{
\psline(-6.062,\n)(6.062,\n)}
\multido{\n=0+1.5}{5}{
\psline(-6.062,-\n)(6.062,-\n)}
\psline(0;0)(7;30)

\rput(0,1){\psline(0;0)(7;30)}
\rput(0,1){\psline(0;0)(7;210)}
\rput(0,2){\psline(0;0)(7;30)}
\rput(0,2){\psline(0;0)(7;210)}
\rput(0,3){\psline(0;0)(6;30)}
\rput(0,3){\psline(0;0)(7;210)}
\rput(0,4){\psline(0;0)(4;30)}
\rput(0,4){\psline(0;0)(7;210)}
\rput(0,5){\psline(0;0)(2;30)}
\rput(0,5){\psline(0;0)(7;210)}
\rput(0,6){\psline(0;0)(7;210)}
\rput(-1.732,6){\psline(0;0)(5;210)}
\rput(-3.464,6){\psline(0;0)(3;210)}
\rput(-5.196,6){\psline(0;0)(1;210)}

\rput(0,-1){\psline(0;0)(7;30)}
\rput(0,-1){\psline(0;0)(7;210)}
\rput(0,-2){\psline(0;0)(7;30)}
\rput(0,-2){\psline(0;0)(7;210)}
\rput(0,-3){\psline(0;0)(7;30)}
\rput(0,-3){\psline(0;0)(6;210)}
\rput(0,-4){\psline(0;0)(7;30)}
\rput(0,-4){\psline(0;0)(4;210)}
\rput(0,-5){\psline(0;0)(7;30)}
\rput(0,-5){\psline(0;0)(2;210)}
\rput(0,-6){\psline(0;0)(7;30)}
\rput(1.732,-6){\psline(0;0)(5;30)}
\rput(3.464,-6){\psline(0;0)(3;30)}
\rput(5.196,-6){\psline(0;0)(1;30)}

\psline(0;0)(6.928;60)
\rput(1.732,0){\psline(0;0)(6.928;60)}
\rput(3.464,0){\psline(0;0)(5.196;60)}
\rput(5.196,0){\psline(0;0)(1.732;60)}
\rput(1.732,0){\psline(0;0)(6.928;240)}
\rput(3.464,0){\psline(0;0)(6.928;240)}
\rput(5.196,0){\psline(0;0)(6.928;240)}
\rput(6.062,-1.5){\psline(0;0)(5.196;240)}
\rput(6.062,-4.5){\psline(0;0)(1.732;240)}
\rput(-1.732,0){\psline(0;0)(6.928;60)}
\rput(-3.464,0){\psline(0;0)(6.928;60)}
\rput(-5.196,0){\psline(0;0)(6.928;60)}
\rput(-1.732,0){\psline(0;0)(6.928;240)}
\rput(-3.464,0){\psline(0;0)(5.196;240)}
\rput(-5.196,0){\psline(0;0)(1.732;240)}
\rput(-6.062,1.5){\psline(0;0)(5.196;60)}
\rput(-6.062,4.5){\psline(0;0)(1.732;60)}

\psline(0;0)(6.928;120)
\psline(0;0)(6.928;300)
\rput(-1.732,0){\psline(0;0)(6.928;120)}
\rput(-3.464,0){\psline(0;0)(5.196;120)}
\rput(-5.196,0){\psline(0;0)(1.732;120)}
\rput(-1.732,0){\psline(0;0)(6.928;300)}
\rput(-3.464,0){\psline(0;0)(6.928;300)}
\rput(-5.196,0){\psline(0;0)(6.928;300)}
\rput(-6.062,-1.5){\psline(0;0)(5.196;300)}
\rput(-6.062,-4.5){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;300)}
\rput(3.464,0){\psline(0;0)(5.196;300)}
\rput(5.196,0){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;120)}
\rput(3.464,0){\psline(0;0)(6.928;120)}
\rput(5.196,0){\psline(0;0)(6.928;120)}
\rput(6.062,1.5){\psline(0;0)(5.196;120)}
\rput(6.062,4.5){\psline(0;0)(1.732;120)}

\rput(0,1){\psline(0;0)(7;150)}
\rput(0,1){\psline(0;0)(7;330)}
\rput(0,2){\psline(0;0)(7;150)}
\rput(0,2){\psline(0;0)(7;330)}
\rput(0,3){\psline(0;0)(6;150)}
\rput(0,3){\psline(0;0)(7;330)}
\rput(0,4){\psline(0;0)(4;150)}
\rput(0,4){\psline(0;0)(7;330)}
\rput(0,5){\psline(0;0)(7;330)}
\rput(0,6){\psline(0;0)(7;330)}
\rput(-1.732,6){\psline(0;0)(2;330)}

\rput(0,-1){\psline(0;0)(7;150)}
\rput(0,-1){\psline(0;0)(7;330)}
\rput(0,-2){\psline(0;0)(7;150)}
\rput(0,-2){\psline(0;0)(7;330)}
\rput(0,-3){\psline(0;0)(7;150)}
\rput(0,-3){\psline(0;0)(6;330)}
\rput(0,-4){\psline(0;0)(7;150)}
\rput(0,-4){\psline(0;0)(4;330)}
\rput(0,-5){\psline(0;0)(7;150)}
\rput(0,-5){\psline(0;0)(2;330)}
\rput(0,-6){\psline(0;0)(7;150)}

\rput(6.062,3.5){\psline(0;0)(5;150)}
\rput(6.062,4.5){\psline(0;0)(3;150)}
\rput(6.062,5.5){\psline(0;0)(1;150)}

\rput(-6.062,-3.5){\psline(0;0)(5;330)}
\rput(-6.062,-4.5){\psline(0;0)(3;330)}
\rput(-6.062,-5.5){\psline(0;0)(1;330)}

\psline(0;0)(7;330)
\psline(0;0)(7;150)
\psline(0;0)(7;210)
\psline(0;0)(6.928;240)

\pspolygon[fillcolor=gray,fillstyle=solid](0,0)(0,1)(0.433,0.75)

\psline[linewidth=1mm](0,1)(0,1.5)
\psline[linewidth=1mm](0,1)(.433,.75)
\psline[linewidth=1mm](0,0)(.866,1.5)
\psline[linewidth=1mm](.866,1.5)(0,1.5)
\psline[linewidth=1mm](-.866,1.5)(0,1)
\psline[linewidth=1mm](0,1)(0,0)
\psline[linewidth=1mm](0,0)(-.866,1.5)

\psline[linewidth=1mm](0,1.5)(0,3)
\psline[linewidth=1mm](0,3)(-1.732,6)
\psline[linewidth=1mm](-.866,1.5)(-3.464,6)

\psline[linewidth=1mm](.433,.75)(1.732,0)
\psline[linewidth=1mm](1.732,0)(6.062,0)
\psline[linewidth=1mm](2.598,1.5)(6.062,1.5)

\psline[linewidth=1mm](-.433,.75)(-1.732,0)
\psline[linewidth=1mm](-1.732,0)(-6.062,0)
\psline[linewidth=1mm](-2.598,1.5)(-6.062,1.5)

\psline[linewidth=1mm](.866,0)(.866,-1.5)
\psline[linewidth=1mm](.866,-1.5)(3.464,-6)
\psline[linewidth=1mm](.866,0)(1.732,0)
\psline[linewidth=1mm](2.598,-1.5)(5.196,-6)

\psline[linewidth=1mm](-.866,0)(-.866,-1.5)
\psline[linewidth=1mm](-.866,-1.5)(-3.464,-6)
\psline[linewidth=1mm](-.866,0)(-1.732,0)
\psline[linewidth=1mm](-2.598,-1.5)(-5.196,-6)

\psline[linewidth=1mm](.433,2.25)(0,3)
\psline[linewidth=1mm](0.866,4.5)(1.732,6)
\psline[linewidth=1mm](.433,2.25)(1.732,3)
\psline[linewidth=1mm](1.732,3)(3.464,6)

\psline[linewidth=1mm](0,0)(0,-6)
\psline[linewidth=1mm](0,0)(.866,-1.5)
\psline[linewidth=1mm](.866,-1.5)(.866,-6)

\psline[linewidth=1mm](1.732,0)(6.062,-2.5)
\psline[linewidth=1mm](2.598,-1.5)(6.062,-3.5)

\psline[linewidth=1mm](-1.732,0)(-6.062,-2.5)
\psline[linewidth=1mm](-2.598,-1.5)(-6.062,-3.5)

\psline[linewidth=1mm](.866,1.5)(6.062,4.5)
\psline[linewidth=1mm](2.598,1.5)(6.062,3.5)

\psline[linewidth=1mm](-.866,1.5)(-6.062,4.5)
\psline[linewidth=1mm](-2.598,1.5)(-6.062,3.5)

\psline[linewidth=1mm](0,3)(0,6)
\psline[linewidth=1mm](.866,4.5)(.866,6)

\psline[linewidth=1mm](.866,1.5)(1.732,3)
\psline[linewidth=1mm](0,0)(-.866,-1.5)

\psline[linewidth=1mm](-.866,.5)(-2.598,1.5)
\psline[linewidth=1mm](.866,.5)(2.598,1.5)
\psline[linewidth=1mm](.866,2.5)(.866,4.5)
\psline[linewidth=1mm](.866,-.5)(2.598,-1.5)
\psline[linewidth=1mm](-.866,-.5)(-2.598,-1.5)

\psline[linewidth=1mm](0,-1)(.433,-.75)

\rput(-1.5,-4.33){{\small ${\bf \tilde{c}_{0}^{1}}$}}
\rput(1.988,-4.31){{\small ${\bf \tilde{c}_{0}^{2}}$}}
\rput(5.452,-4.31){{\small ${\bf \tilde{c}_{0}^{3}}$}}
\rput(5.452,-1.31){{\small ${\bf \tilde{c}_{0}^{4}}$}}
\rput(3.69,1.7){{\small ${\bf \tilde{c}_{0}^{5}}$}}
\rput(2.824,3.2){{\small ${\bf \tilde{c}_{0}^{6}}$}}
\rput(1.1,5.75){{\small ${\bf \tilde{c}_{0}^{7}}$}}
\rput(-0.23,4.67){{\small ${\bf \tilde{c}_{0}^{8}}$}}
\rput(-2.372,3.2){{\small ${\bf \tilde{c}_{0}^{9}}$}}
\rput(-4.97,1.7){{\small ${\bf \tilde{c}_{0}^{10}}$}}

\rput(-4.97,-1.3){{\small ${\bf \tilde{c}_{0}^{11}}$}}
\rput(-4.97,-4.3){{\small ${\bf \tilde{c}_{0}^{12}}$}}

\rput(2.3,-2.33){{\small ${\bf  \tilde{c}_{1}^{1}}$}}
\rput(3.2,.73){{\small ${\bf \tilde{c}_{1}^{2}}$}}
\rput(1.5,4.34){{\small ${\bf \tilde{c}_{1}^{3}}$}}
\rput(-1.5,4.34){{\small ${\bf \tilde{c}_{1}^{4}}$}}
\rput(-3.2,.73){{\small ${\bf \tilde{c}_{1}^{5}}$}}
\rput(-2.3,-2.33){{\small ${\bf  \tilde{c}_{1}^{6}}$}}

\rput(0.3,-4.33){{\small ${\bf  \tilde{c}_{2}^{1}}$}}
\rput(3.2,-1.33){{\small ${\bf \tilde{c}_{2}^{2}}$}}
\rput(3.2,2.34){{\small ${\bf \tilde{c}_{2}^{3}}$}}
\rput(0.3,4.33){{\small ${\bf \tilde{c}_{2}^{4}}$}}
\rput(-3.4,2.34){{\small ${\bf \tilde{c}_{2}^{5}}$}}
\rput(-3.2,-1.33){{\small ${\bf \tilde{c}_{2}^{6}}$}}

\rput(.16,-.63){{\small ${\bf \tilde{c}_{3}^{1}}$}}

\rput(.6,.19){{\small ${\bf \tilde{c}_{4}^{1}}$}}
\rput(.4,1.93){{\small ${\bf \tilde{c}_{4}^{2}}$}}
\rput(-.49,.23){{\small ${\bf \tilde{c}_{4}^{3}}$}}

\rput(.3,1.1){{\small ${\bf \tilde{c}_{5}^{1}}$}}
\rput(-.23,.73){{\small ${\bf \tilde{c}_{5}^{2}}$}}

\rput(.17,.68){{\small ${\bf \tilde{c}_{6}^{1}}$}}

\rput(0,-7){\textsc{Figure 10}. Partition of $\tilde{G}_{2}$ into cells}

\end{pspicture}
\end{center}

\newpage

\begin{center}
\begin{pspicture}(-1.3,-1.5)(13,13)
\psset{unit=.7pt}

\pscircle(-100,0){10}
\rput(-100,0){{\small $u_{0}^{1}$}}
\pscircle(-60,0){10}
\rput(-60,0){{\small $u_{0}^{2}$}}

\pscircle(0,0){10}
\rput(0,0){{\small $u_{0}^{3}$}}
\pscircle(40,0){10}
\rput(40,0){{\small $u_{0}^{4}$}}
\pscircle(100,0){10}
\rput(100,0){{\small $u_{0}^{5}$}}
\pscircle(140,0){10}
\rput(140,0){{\small $u_{0}^{6}$}}

\pscircle(200,0){10}
\rput(200,0){{\small $u_{0}^{7}$}}
\pscircle(240,0){10}
\rput(240,0){{\small $u_{0}^{8}$}}

\pscircle(300,0){10}
\rput(300,0){{\small $u_{0}^{9}$}}
\pscircle(340,0){10}
\rput(340,0){{\small $u_{0}^{10}$}}

\pscircle(400,0){10}
\rput(400,0){{\small $u_{0}^{11}$}}
\pscircle(440,0){10}
\rput(440,0){{\small $u_{0}^{12}$}}

\pscircle(500,0){10}
\rput(500,0){{\small $u_{0}^{1}$}}
\pscircle(540,0){10}
\rput(540,0){{\small $u_{0}^{2}$}}

\pscircle(20,100){10}
\rput(20,100){{\scriptsize $u_{1}^{1}$}}

\pscircle(120,100){10}
\rput(120,100){{\scriptsize $u_{1}^{2}$}}

\pscircle(220,100){10}
\rput(220,100){{\scriptsize $u_{1}^{3}$}}

\pscircle(270,100){10}
\rput(270,100){{\scriptsize $u_{1}^{4}$}}

\pscircle(320,100){10}
\rput(320,100){{\scriptsize $u_{1}^{5}$}}

\pscircle(420,100){10}
\rput(420,100){{\scriptsize $u_{1}^{6}$}}

\pscircle(-5,250){10}
\rput(-5,250){{\scriptsize $u_{3}^{1}$}}

\pscircle(-80,200){10}
\rput(-80,200){{\scriptsize $u_{2}^{1}$}}

\pscircle(20,200){10}
\rput(20,200){{\scriptsize $u_{2}^{2}$}}

\pscircle(120,200){10}
\rput(120,200){{\scriptsize $u_{2}^{3}$}}

\pscircle(220,200){10}
\rput(220,200){{\scriptsize $u_{2}^{4}$}}

\pscircle(320,200){10}
\rput(320,200){{\scriptsize $u_{2}^{5}$}}

\pscircle(420,200){10}
\rput(420,200){{\scriptsize $u_{2}^{6}$}}

\pscircle(70,300){10}
\rput(70,300){{\tiny $u_{4}^{1}$}}

\pscircle(245,300){10}
\rput(245,300){{\tiny $u_{4}^{2}$}}

\pscircle(370,300){10}
\rput(370,300){{\tiny $u_{4}^{3}$}}

\pscircle(280,400){10}
\rput(280,400){{\scriptsize$u_{5}^{1}$}}

\pscircle(335,400){10}
\rput(335,400){{\scriptsize$u_{5}^{2}$}}

\pscircle(307.5,350){3}

\pscircle(307.5,450){10}
\rput(307.5,450){{\scriptsize$u_{6}^{1}$}}

\psline(20,90)(-60,10)

\psline(20,90)(40,10)

\psline(20,90)(-100,10)

\psline(20,90)(0,10)

\psline(20,90)(140,10)

\psline(120,90)(40,10)

\psline(120,90)(140,10)

\psline(120,90)(100,10)

\psline(220,90)(140,10)

\psline(220,90)(240,10)

\psline(220,90)(200,10)

\psline(220,90)(40,10)

\psline(220,90)(300,10)

\psline(270,90)(240,10)

\psline(270,90)(300,10)

\psline(320,90)(340,10)

\psline(320,90)(400,10)

\psline(320,90)(300,10)

\psline(320,90)(500,10)

\psline(420,90)(440,10)

\psline(420,90)(500,10)

\psline(420,90)(400,10)

\psline(420,90)(300,10)

\psline(-5,240)(-80,210)
\psline(-80,190)(-100,10)

\psline(-80,190)(-60,10)

\psline(20,190)(20,110)

\psline(120,190)(120,110)

\psline(220,190)(220,110)

\psline(320,190)(320,110)

\psline(420,190)(420,110)

\psline(70,290)(-5,260)

\psline(70,290)(20,210)

\psline(70,290)(120,210)

\psline(245,290)(120,210)

\psline(245,290)(220,210)

\psline(245,290)(270,110)

\psline(370,290)(320,210)

\psline(370,290)(420,210)

\psline(280,390)(245,310)

\psline(335,390)(370,310)

\psline(280,390)(307.5,353)
\psline(307.5,347)(270,110)
\psline(335,390)(307.5,353)

\psline(307.5,440)(280,410)

\psline(307.5,440)(335,410)

\psline(307.5,440)(70,310)
\rput(200,-50){Figure 11. Order $\preceq$ on $U$}

\end{pspicture}
\end{center}

\vspace{2cm}

Let $w=s_{1}s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1}s_{2}$, and $w_{1}=s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}$. In the following table we have
$$y\in \{zw^{n}| z\in Y(w), n\in\mathbb{N}\} \text{ and } y_{1}\in \{yw_{1}^{n}| y\in Y(w_{1}), n\in\mathbb{N}\} $$

\newpage

{\footnotesize
\begin{table}[h!] \caption{Condition {\bf I5} for $1<r<3/2$}
\label{PcG}
\begin{textblock}{21}(0,4)
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{1}^{1} & s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{a+b} C_{u_{0}^{1}}\\\hline
u_{1}^{1} & s_{3}s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{a+b} T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{1} & y_{1}w_{1} & T_{xu} +v^{a+b} T_{y_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{1} & y_{1}w_{1}s_{3}s_{2}s_{1} & T_{xu}+v^{a+b}T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{1}^{3} & s_{1}s_{2}s_{1} & T_{xu} +v^{a+b} C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{a} C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{3}s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{a} T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & y_{1}w_{1} & T_{xu} +v^{a} T_{y_{1}s_{2}s_{3}}C_{u_{0}^{6}}+T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+v^{a+b}T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{2}s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+v^{a+b}T_{s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+v^{a+b}T_{s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+v^{a+b}T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+v^{a+b}T_{s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & y_{1}w_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{y_{1}s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+v^{a}T_{ys_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline

u_{1}^{6} & s_{1}s_{2}s_{1} & T_{xu} +v^{a+b} C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{a} C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{3}s_{2}s_{1}s_{2}s_{1} & T_{xu} +v^{a} T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & y_{1}w_{1}& T_{xu} +v^{a} T_{ys_{2}s_{3}}C_{u_{0}^{1}}+T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+v^{a+b}T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+v^{a+b}T_{s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+v^{a+b}T_{s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+v^{a+b}T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+v^{a+b}T_{s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & y_{1}w_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{y_{1}s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+v^{a}T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{1} & s_{1}s_{2} & T_{xu} +v^{a-b} C_{u_{0}^{1}}\\\hline
u_{2}^{1} & s_{2}s_{1}s_{2} & T_{xu} +v^{a} C_{u_{0}^{1}}\\\hline
u_{2}^{1} & s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{a} T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{1} & s_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +(v^{2a}-v^{2a-2b}) T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{1} & ys_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +(v^{2a}-v^{2a-2b}) T_{ys_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{2} & s_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{a+b} T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{2} & ys_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{a+b} T_{ys_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{4} & s_{2}s_{1}s_{2} & T_{xu} +C_{u_{0}^{6}}\\\hline
u_{2}^{4} & s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{4} & s_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{a}T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{4} & ys_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{a}T_{ys_{3}}C_{u_{0}^{6}}\\\hline

u_{2}^{6} & s_{2}s_{1}s_{2} & T_{xu} +C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{a}T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & ys_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{a}T_{ys_{3}}C_{u_{0}^{1}}\\\hline

 \end{array}$
 \end{textblock}
\end{table}}

$\ $\\

\newpage

\item {\bf Case ${\bf r=1}$}

\begin{center}
\begin{pspicture}(-6,-6)(6,9)
\psset{unit=1.3cm}

\SpecialCoor
\psline(0,-6)(0,6)
\multido{\n=1+1}{7}{
\psline(\n;30)(\n;330)}
\rput(1;30){\psline(0,0)(0,5.5)}
\rput(1;330){\psline(0,0)(0,-5.5)}
\rput(2;30){\psline(0,0)(0,5)}
\rput(2;330){\psline(0,0)(0,-5)}
\rput(3;30){\psline(0,0)(0,4.5)}
\rput(3;330){\psline(0,0)(0,-4.5)}
\rput(4;30){\psline(0,0)(0,4)}
\rput(4;330){\psline(0,0)(0,-4)}
\rput(5;30){\psline(0,0)(0,3.5)}
\rput(5;330){\psline(0,0)(0,-3.5)}
\rput(6;30){\psline(0,0)(0,3)}
\rput(6;330){\psline(0,0)(0,-3)}
\rput(7;30){\psline(0,0)(0,2.5)}
\rput(7;330){\psline(0,0)(0,-2.5)}
\multido{\n=1+1}{7}{
\psline(\n;150)(\n;210)}
\rput(1;150){\psline(0,0)(0,5.5)}
\rput(1;210){\psline(0,0)(0,-5.5)}
\rput(2;150){\psline(0,0)(0,5)}
\rput(2;210){\psline(0,0)(0,-5)}
\rput(3;150){\psline(0,0)(0,4.5)}
\rput(3;210){\psline(0,0)(0,-4.5)}
\rput(4;150){\psline(0,0)(0,4)}
\rput(4;210){\psline(0,0)(0,-4)}
\rput(5;150){\psline(0,0)(0,3.5)}
\rput(5;210){\psline(0,0)(0,-3.5)}
\rput(6;150){\psline(0,0)(0,3)}
\rput(6;210){\psline(0,0)(0,-3)}
\rput(7;150){\psline(0,0)(0,2.5)}
\rput(7;210){\psline(0,0)(0,-2.5)}
\multido{\n=1.5+1.5}{4}{
\psline(-6.062,\n)(6.062,\n)}
\multido{\n=0+1.5}{5}{
\psline(-6.062,-\n)(6.062,-\n)}
\psline(0;0)(7;30)

\rput(0,1){\psline(0;0)(7;30)}
\rput(0,1){\psline(0;0)(7;210)}
\rput(0,2){\psline(0;0)(7;30)}
\rput(0,2){\psline(0;0)(7;210)}
\rput(0,3){\psline(0;0)(6;30)}
\rput(0,3){\psline(0;0)(7;210)}
\rput(0,4){\psline(0;0)(4;30)}
\rput(0,4){\psline(0;0)(7;210)}
\rput(0,5){\psline(0;0)(2;30)}
\rput(0,5){\psline(0;0)(7;210)}
\rput(0,6){\psline(0;0)(7;210)}
\rput(-1.732,6){\psline(0;0)(5;210)}
\rput(-3.464,6){\psline(0;0)(3;210)}
\rput(-5.196,6){\psline(0;0)(1;210)}

\rput(0,-1){\psline(0;0)(7;30)}
\rput(0,-1){\psline(0;0)(7;210)}
\rput(0,-2){\psline(0;0)(7;30)}
\rput(0,-2){\psline(0;0)(7;210)}
\rput(0,-3){\psline(0;0)(7;30)}
\rput(0,-3){\psline(0;0)(6;210)}
\rput(0,-4){\psline(0;0)(7;30)}
\rput(0,-4){\psline(0;0)(4;210)}
\rput(0,-5){\psline(0;0)(7;30)}
\rput(0,-5){\psline(0;0)(2;210)}
\rput(0,-6){\psline(0;0)(7;30)}
\rput(1.732,-6){\psline(0;0)(5;30)}
\rput(3.464,-6){\psline(0;0)(3;30)}
\rput(5.196,-6){\psline(0;0)(1;30)}

\psline(0;0)(6.928;60)
\rput(1.732,0){\psline(0;0)(6.928;60)}
\rput(3.464,0){\psline(0;0)(5.196;60)}
\rput(5.196,0){\psline(0;0)(1.732;60)}
\rput(1.732,0){\psline(0;0)(6.928;240)}
\rput(3.464,0){\psline(0;0)(6.928;240)}
\rput(5.196,0){\psline(0;0)(6.928;240)}
\rput(6.062,-1.5){\psline(0;0)(5.196;240)}
\rput(6.062,-4.5){\psline(0;0)(1.732;240)}
\rput(-1.732,0){\psline(0;0)(6.928;60)}
\rput(-3.464,0){\psline(0;0)(6.928;60)}
\rput(-5.196,0){\psline(0;0)(6.928;60)}
\rput(-1.732,0){\psline(0;0)(6.928;240)}
\rput(-3.464,0){\psline(0;0)(5.196;240)}
\rput(-5.196,0){\psline(0;0)(1.732;240)}
\rput(-6.062,1.5){\psline(0;0)(5.196;60)}
\rput(-6.062,4.5){\psline(0;0)(1.732;60)}

\psline(0;0)(6.928;120)
\psline(0;0)(6.928;300)
\rput(-1.732,0){\psline(0;0)(6.928;120)}
\rput(-3.464,0){\psline(0;0)(5.196;120)}
\rput(-5.196,0){\psline(0;0)(1.732;120)}
\rput(-1.732,0){\psline(0;0)(6.928;300)}
\rput(-3.464,0){\psline(0;0)(6.928;300)}
\rput(-5.196,0){\psline(0;0)(6.928;300)}
\rput(-6.062,-1.5){\psline(0;0)(5.196;300)}
\rput(-6.062,-4.5){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;300)}
\rput(3.464,0){\psline(0;0)(5.196;300)}
\rput(5.196,0){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;120)}
\rput(3.464,0){\psline(0;0)(6.928;120)}
\rput(5.196,0){\psline(0;0)(6.928;120)}
\rput(6.062,1.5){\psline(0;0)(5.196;120)}
\rput(6.062,4.5){\psline(0;0)(1.732;120)}

\rput(0,1){\psline(0;0)(7;150)}
\rput(0,1){\psline(0;0)(7;330)}
\rput(0,2){\psline(0;0)(7;150)}
\rput(0,2){\psline(0;0)(7;330)}
\rput(0,3){\psline(0;0)(6;150)}
\rput(0,3){\psline(0;0)(7;330)}
\rput(0,4){\psline(0;0)(4;150)}
\rput(0,4){\psline(0;0)(7;330)}
\rput(0,5){\psline(0;0)(7;330)}
\rput(0,6){\psline(0;0)(7;330)}
\rput(-1.732,6){\psline(0;0)(2;330)}

\rput(0,-1){\psline(0;0)(7;150)}
\rput(0,-1){\psline(0;0)(7;330)}
\rput(0,-2){\psline(0;0)(7;150)}
\rput(0,-2){\psline(0;0)(7;330)}
\rput(0,-3){\psline(0;0)(7;150)}
\rput(0,-3){\psline(0;0)(6;330)}
\rput(0,-4){\psline(0;0)(7;150)}
\rput(0,-4){\psline(0;0)(4;330)}
\rput(0,-5){\psline(0;0)(7;150)}
\rput(0,-5){\psline(0;0)(2;330)}
\rput(0,-6){\psline(0;0)(7;150)}

\rput(6.062,3.5){\psline(0;0)(5;150)}
\rput(6.062,4.5){\psline(0;0)(3;150)}
\rput(6.062,5.5){\psline(0;0)(1;150)}

\rput(-6.062,-3.5){\psline(0;0)(5;330)}
\rput(-6.062,-4.5){\psline(0;0)(3;330)}
\rput(-6.062,-5.5){\psline(0;0)(1;330)}

\psline(0;0)(7;330)
\psline(0;0)(7;150)
\psline(0;0)(7;210)
\psline(0;0)(6.928;240)

\pspolygon[fillcolor=gray,fillstyle=solid](0,0)(0,1)(0.433,0.75)

\psline[linewidth=1mm](0,1)(0,1.5)
\psline[linewidth=1mm](0,1)(.433,.75)
\psline[linewidth=1mm](0,0)(.866,1.5)
\psline[linewidth=1mm](-.866,1.5)(0,1)
\psline[linewidth=1mm](0,1)(0,0)
\psline[linewidth=1mm](-.433,0.75)(-.866,1.5)

\psline[linewidth=1mm](0,1.5)(0,3)
\psline[linewidth=1mm](0,3)(-1.732,6)
\psline[linewidth=1mm](-.866,1.5)(-3.464,6)

\psline[linewidth=1mm](.433,.75)(1.732,0)
\psline[linewidth=1mm](1.732,0)(6.062,0)
\psline[linewidth=1mm](2.598,1.5)(6.062,1.5)

\psline[linewidth=1mm](-.433,.75)(-1.732,0)
\psline[linewidth=1mm](-1.732,0)(-6.062,0)
\psline[linewidth=1mm](-2.598,1.5)(-6.062,1.5)

\psline[linewidth=1mm](.866,0)(.866,-1.5)
\psline[linewidth=1mm](.866,-1.5)(3.464,-6)
\psline[linewidth=1mm](.866,0)(1.732,0)
\psline[linewidth=1mm](2.598,-1.5)(5.196,-6)

\psline[linewidth=1mm](-.866,0)(-.866,-1.5)
\psline[linewidth=1mm](-.866,-1.5)(-3.464,-6)
\psline[linewidth=1mm](-.866,0)(-1.732,0)
\psline[linewidth=1mm](-2.598,-1.5)(-5.196,-6)

\psline[linewidth=1mm](.433,2.25)(0,3)
\psline[linewidth=1mm](0.866,4.5)(1.732,6)
\psline[linewidth=1mm](.433,2.25)(1.732,3)
\psline[linewidth=1mm](1.732,3)(3.464,6)

\psline[linewidth=1mm](0,0)(0,-6)
\psline[linewidth=1mm](.433,-0.75)(.866,-1.5)
\psline[linewidth=1mm](.866,-1.5)(.866,-6)

\psline[linewidth=1mm](1.732,0)(6.062,-2.5)
\psline[linewidth=1mm](2.598,-1.5)(6.062,-3.5)

\psline[linewidth=1mm](-1.732,0)(-6.062,-2.5)
\psline[linewidth=1mm](-2.598,-1.5)(-6.062,-3.5)

\psline[linewidth=1mm](.866,1.5)(6.062,4.5)
\psline[linewidth=1mm](2.598,1.5)(6.062,3.5)

\psline[linewidth=1mm](-.866,1.5)(-6.062,4.5)
\psline[linewidth=1mm](-2.598,1.5)(-6.062,3.5)

\psline[linewidth=1mm](0,3)(0,6)
\psline[linewidth=1mm](.866,4.5)(.866,6)

\psline[linewidth=1mm](.866,1.5)(1.732,3)
\psline[linewidth=1mm](0,0)(-.866,-1.5)

\psline[linewidth=1mm](-.866,.5)(-2.598,1.5)
\psline[linewidth=1mm](.866,.5)(2.598,1.5)
\psline[linewidth=1mm](.866,2.5)(.866,4.5)
\psline[linewidth=1mm](.866,-.5)(2.598,-1.5)
\psline[linewidth=1mm](-.866,-.5)(-2.598,-1.5)

\psline[linewidth=1mm](0,-1)(.433,-.75)

\rput(-1.5,-4.33){{\small ${\bf \tilde{c}_{0}^{1}}$}}
\rput(1.988,-4.31){{\small ${\bf \tilde{c}_{0}^{2}}$}}
\rput(5.452,-4.31){{\small ${\bf \tilde{c}_{0}^{3}}$}}
\rput(5.452,-1.31){{\small ${\bf \tilde{c}_{0}^{4}}$}}
\rput(3.69,1.7){{\small ${\bf \tilde{c}_{0}^{5}}$}}
\rput(2.824,3.2){{\small ${\bf \tilde{c}_{0}^{6}}$}}
\rput(1.1,5.75){{\small ${\bf \tilde{c}_{0}^{7}}$}}
\rput(-0.23,4.67){{\small ${\bf \tilde{c}_{0}^{8}}$}}
\rput(-2.372,3.2){{\small ${\bf \tilde{c}_{0}^{9}}$}}
\rput(-4.97,1.7){{\small ${\bf \tilde{c}_{0}^{10}}$}}

\rput(-4.97,-1.3){{\small ${\bf \tilde{c}_{0}^{11}}$}}
\rput(-4.97,-4.3){{\small ${\bf \tilde{c}_{0}^{12}}$}}

\rput(2.3,-2.33){{\small ${\bf  \tilde{c}_{1}^{1}}$}}
\rput(3.2,.73){{\small ${\bf \tilde{c}_{1}^{2}}$}}
\rput(1.5,4.34){{\small ${\bf \tilde{c}_{1}^{3}}$}}
\rput(-1.5,4.34){{\small ${\bf \tilde{c}_{1}^{4}}$}}
\rput(-3.2,.73){{\small ${\bf \tilde{c}_{1}^{5}}$}}
\rput(-2.3,-2.33){{\small ${\bf  \tilde{c}_{1}^{6}}$}}

\rput(0.3,-4.33){{\small ${\bf  \tilde{c}_{2}^{1}}$}}
\rput(3.2,-1.33){{\small ${\bf \tilde{c}_{2}^{2}}$}}
\rput(3.2,2.34){{\small ${\bf \tilde{c}_{2}^{3}}$}}
\rput(0.3,4.33){{\small ${\bf \tilde{c}_{2}^{4}}$}}
\rput(-3.4,2.34){{\small ${\bf \tilde{c}_{2}^{5}}$}}
\rput(-3.2,-1.33){{\small ${\bf \tilde{c}_{2}^{6}}$}}

\rput(.6,.19){{\small ${\bf \tilde{c}_{4}^{1}}$}}
\rput(.4,1.93){{\small ${\bf \tilde{c}_{4}^{2}}$}}
\rput(-.49,.23){{\small ${\bf \tilde{c}_{4}^{3}}$}}

\rput(.17,.68){{\small ${\bf \tilde{c}_{6}^{1}}$}}

\rput(0,-7){\textsc{Figure 12}. Partition of $\tilde{G}_{2}$ into cells}

\end{pspicture}
\end{center}

\newpage

\begin{center}

\begin{pspicture}(-1.3,-1.5)(13,13)
\psset{unit=.7pt}
\pscircle(-100,0){10}
\rput(-100,0){{\small $u_{0}^{1}$}}
\pscircle(-60,0){10}
\rput(-60,0){{\small $u_{0}^{2}$}}

\pscircle(0,0){10}
\rput(0,0){{\small $u_{0}^{3}$}}
\pscircle(40,0){10}
\rput(40,0){{\small $u_{0}^{4}$}}
\pscircle(100,0){10}
\rput(100,0){{\small $u_{0}^{5}$}}
\pscircle(140,0){10}
\rput(140,0){{\small $u_{0}^{6}$}}

\pscircle(200,0){10}
\rput(200,0){{\small $u_{0}^{7}$}}
\pscircle(240,0){10}
\rput(240,0){{\small $u_{0}^{8}$}}

\pscircle(300,0){10}
\rput(300,0){{\small $u_{0}^{9}$}}
\pscircle(340,0){10}
\rput(340,0){{\small $u_{0}^{10}$}}

\pscircle(400,0){10}
\rput(400,0){{\small $u_{0}^{11}$}}
\pscircle(440,0){10}
\rput(440,0){{\small $u_{0}^{12}$}}

\pscircle(500,0){10}
\rput(500,0){{\small $u_{0}^{1}$}}
\pscircle(540,0){10}
\rput(540,0){{\small $u_{0}^{2}$}}

\pscircle(20,100){10}
\rput(20,100){{\scriptsize $u_{1}^{1}$}}

\pscircle(120,100){10}
\rput(120,100){{\scriptsize $u_{1}^{2}$}}

\pscircle(220,100){10}
\rput(220,100){{\scriptsize $u_{1}^{3}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](270,100){10}
\rput(270,100){{\scriptsize $u_{1}^{4}$}}

\pscircle(320,100){10}
\rput(320,100){{\scriptsize $u_{1}^{5}$}}

\pscircle(420,100){10}
\rput(420,100){{\scriptsize $u_{1}^{6}$}}

\pscircle(-80,200){10}
\rput(-80,200){{\scriptsize $u_{2}^{1}$}}

\pscircle(20,200){10}
\rput(20,200){{\scriptsize $u_{2}^{2}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](120,200){10}
\rput(120,200){{\scriptsize $u_{2}^{3}$}}

\pscircle(220,200){10}
\rput(220,200){{\scriptsize $u_{2}^{4}$}}

\pscircle(320,200){10}
\rput(320,200){{\scriptsize $u_{2}^{5}$}}

\pscircle(420,200){10}
\rput(420,200){{\scriptsize $u_{2}^{6}$}}

\pscircle(70,300){10}
\rput(70,300){{\tiny $u_{4}^{1}$}}

\pscircle(245,300){10}
\rput(245,300){{\tiny $u_{4}^{2}$}}

\pscircle(370,300){10}
\rput(370,300){{\tiny $u_{4}^{3}$}}

\pscircle(307.5,450){10}
\rput(307.5,450){{\scriptsize$e$}}

\psline(20,90)(-60,10)

\psline(20,90)(40,10)

\psline(20,90)(-100,10)

\psline(20,90)(0,10)

\psline(120,90)(40,10)

\psline(120,90)(140,10)

\psline(120,90)(100,10)

\psline(220,90)(140,10)

\psline(220,90)(240,10)

\psline(220,90)(200,10)

\psline(220,90)(40,10)

\psline(220,90)(300,10)

\psline(270,90)(240,10)

\psline(270,90)(300,10)

\psline(320,90)(340,10)

\psline(320,90)(400,10)

\psline(320,90)(300,10)

\psline(320,90)(500,10)

\psline(420,90)(440,10)

\psline(420,90)(500,10)

\psline(420,90)(400,10)

\psline(-80,190)(-100,10)

\psline(-80,190)(-60,10)

\psline(-80,190)(20,110)

\psline(20,190)(20,110)

\psline[linecolor=black](20,190)(120,110)

\psline(120,190)(120,110)

\psline[linecolor=black](220,190)(270,110)

\psline[linecolor=black](220,190)(120,110)

\psline(220,190)(220,110)

\psline(320,190)(320,110)

\psline[linecolor=black](320,190)(270,110)

\psline(420,190)(420,110)

\psline[linecolor=black](420,190)(320,110)

\psline(70,290)(-80,210)

\psline(70,290)(20,210)

\psline(70,290)(120,210)

\psline(245,290)(120,210)

\psline(245,290)(220,210)

\psline(370,290)(320,210)

\psline(370,290)(420,210)

\psline(307.5,440)(245,310)

\psline(307.5,440)(370,310)

\psline(307.5,440)(70,310)

\rput(200,-50){Figure 13. Order $\preceq$ on $U$}

\end{pspicture}
\end{center}

\vspace{2cm}

Let $w=s_{1}s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1}s_{2}$, and $w_{1}=s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}$. In the following table we have
$$y\in \{zw^{n}| z\in Y(w), n\in\mathbb{N}\} \text{ and } y_{1}\in \{yw_{1}^{n}| y\in Y(w_{1}), n\in\mathbb{N}\} $$

\newpage

\vspace{2cm}
{\footnotesize
\begin{table}[t] \caption{Condition {\bf I5} for $r=1$}
\label{PcG}
\begin{textblock}{21}(0,4)
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{1}^{1} & s_{2}s_{1}s_{2}s_{1} & T_{xu} + C_{u_{0}^{1}}\\\hline
u_{1}^{1} & s_{3}s_{2}s_{1}s_{2}s_{1} & T_{xu} + T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{1} & y_{1}w_{1}& T_{xu} + T_{y_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{1} & y_{1}w_{1}s_{3}s_{2}s_{1} & T_{xu}+T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{1}^{3} & s_{1}s_{2}s_{1} & T_{xu} + C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{2}s_{1}s_{2}s_{1} & T_{xu} +v C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{3}s_{2}s_{1}s_{2}s_{1} & T_{xu} +v T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & y_{1}w_{1}& T_{xu} +v T_{y_{1}s_{2}s_{3}}C_{u_{0}^{6}}+T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline

u_{1}^{3} & s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{2}s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+T_{s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+T_{s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+T_{s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & y_{1}w_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{y_{1}s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+T_{ys_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline

u_{1}^{6} & s_{1}s_{2}s_{1} & T_{xu} + C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{1}s_{2}s_{1} & T_{xu} +v C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{3}s_{2}s_{1}s_{2}s_{1} & T_{xu} +v T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & y_{1}w_{1}& T_{xu} +v T_{y_{1}s_{2}s_{3}}C_{u_{0}^{1}}+T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+T_{s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+T_{s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+T_{s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & y_{1}w_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{y_{1}s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+vT_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{1} & s_{1}s_{2} & T_{xu} + C_{u_{0}^{1}}\\\hline
u_{2}^{1} & s_{2}s_{1}s_{2} & T_{xu} +v C_{u_{0}^{1}}\\\hline
u_{2}^{1} & s_{3}s_{2}s_{1}s_{2} & T_{xu} +v T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{1} & s_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{2} T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{1} & ys_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{2} T_{ys_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{2} & ys_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} + T_{ys_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{4} & s_{2}s_{1}s_{2} & T_{xu} +C_{u_{0}^{6}}\\\hline
u_{2}^{4} & s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{4} & s_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{}T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{4} & ys_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{}T_{ys_{3}}C_{u_{0}^{6}}\\\hline

u_{2}^{6} & s_{2}s_{1}s_{2} & T_{xu} +C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{}T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & ys_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{}T_{ys_{3}}C_{u_{0}^{1}}\\\hline

 \end{array}$
\end{textblock}
\end{table}}

$\ $\\

\newpage

\item {\bf Case ${\bf 0<r<1}$}

\begin{center}
\begin{pspicture}(-6,-6)(6,9)
\psset{unit=1.3cm}

\SpecialCoor
\psline(0,-6)(0,6)
\multido{\n=1+1}{7}{
\psline(\n;30)(\n;330)}
\rput(1;30){\psline(0,0)(0,5.5)}
\rput(1;330){\psline(0,0)(0,-5.5)}
\rput(2;30){\psline(0,0)(0,5)}
\rput(2;330){\psline(0,0)(0,-5)}
\rput(3;30){\psline(0,0)(0,4.5)}
\rput(3;330){\psline(0,0)(0,-4.5)}
\rput(4;30){\psline(0,0)(0,4)}
\rput(4;330){\psline(0,0)(0,-4)}
\rput(5;30){\psline(0,0)(0,3.5)}
\rput(5;330){\psline(0,0)(0,-3.5)}
\rput(6;30){\psline(0,0)(0,3)}
\rput(6;330){\psline(0,0)(0,-3)}
\rput(7;30){\psline(0,0)(0,2.5)}
\rput(7;330){\psline(0,0)(0,-2.5)}
\multido{\n=1+1}{7}{
\psline(\n;150)(\n;210)}
\rput(1;150){\psline(0,0)(0,5.5)}
\rput(1;210){\psline(0,0)(0,-5.5)}
\rput(2;150){\psline(0,0)(0,5)}
\rput(2;210){\psline(0,0)(0,-5)}
\rput(3;150){\psline(0,0)(0,4.5)}
\rput(3;210){\psline(0,0)(0,-4.5)}
\rput(4;150){\psline(0,0)(0,4)}
\rput(4;210){\psline(0,0)(0,-4)}
\rput(5;150){\psline(0,0)(0,3.5)}
\rput(5;210){\psline(0,0)(0,-3.5)}
\rput(6;150){\psline(0,0)(0,3)}
\rput(6;210){\psline(0,0)(0,-3)}
\rput(7;150){\psline(0,0)(0,2.5)}
\rput(7;210){\psline(0,0)(0,-2.5)}
\multido{\n=1.5+1.5}{4}{
\psline(-6.062,\n)(6.062,\n)}
\multido{\n=0+1.5}{5}{
\psline(-6.062,-\n)(6.062,-\n)}
\psline(0;0)(7;30)

\rput(0,1){\psline(0;0)(7;30)}
\rput(0,1){\psline(0;0)(7;210)}
\rput(0,2){\psline(0;0)(7;30)}
\rput(0,2){\psline(0;0)(7;210)}
\rput(0,3){\psline(0;0)(6;30)}
\rput(0,3){\psline(0;0)(7;210)}
\rput(0,4){\psline(0;0)(4;30)}
\rput(0,4){\psline(0;0)(7;210)}
\rput(0,5){\psline(0;0)(2;30)}
\rput(0,5){\psline(0;0)(7;210)}
\rput(0,6){\psline(0;0)(7;210)}
\rput(-1.732,6){\psline(0;0)(5;210)}
\rput(-3.464,6){\psline(0;0)(3;210)}
\rput(-5.196,6){\psline(0;0)(1;210)}

\rput(0,-1){\psline(0;0)(7;30)}
\rput(0,-1){\psline(0;0)(7;210)}
\rput(0,-2){\psline(0;0)(7;30)}
\rput(0,-2){\psline(0;0)(7;210)}
\rput(0,-3){\psline(0;0)(7;30)}
\rput(0,-3){\psline(0;0)(6;210)}
\rput(0,-4){\psline(0;0)(7;30)}
\rput(0,-4){\psline(0;0)(4;210)}
\rput(0,-5){\psline(0;0)(7;30)}
\rput(0,-5){\psline(0;0)(2;210)}
\rput(0,-6){\psline(0;0)(7;30)}
\rput(1.732,-6){\psline(0;0)(5;30)}
\rput(3.464,-6){\psline(0;0)(3;30)}
\rput(5.196,-6){\psline(0;0)(1;30)}

\psline(0;0)(6.928;60)
\rput(1.732,0){\psline(0;0)(6.928;60)}
\rput(3.464,0){\psline(0;0)(5.196;60)}
\rput(5.196,0){\psline(0;0)(1.732;60)}
\rput(1.732,0){\psline(0;0)(6.928;240)}
\rput(3.464,0){\psline(0;0)(6.928;240)}
\rput(5.196,0){\psline(0;0)(6.928;240)}
\rput(6.062,-1.5){\psline(0;0)(5.196;240)}
\rput(6.062,-4.5){\psline(0;0)(1.732;240)}
\rput(-1.732,0){\psline(0;0)(6.928;60)}
\rput(-3.464,0){\psline(0;0)(6.928;60)}
\rput(-5.196,0){\psline(0;0)(6.928;60)}
\rput(-1.732,0){\psline(0;0)(6.928;240)}
\rput(-3.464,0){\psline(0;0)(5.196;240)}
\rput(-5.196,0){\psline(0;0)(1.732;240)}
\rput(-6.062,1.5){\psline(0;0)(5.196;60)}
\rput(-6.062,4.5){\psline(0;0)(1.732;60)}

\psline(0;0)(6.928;120)
\psline(0;0)(6.928;300)
\rput(-1.732,0){\psline(0;0)(6.928;120)}
\rput(-3.464,0){\psline(0;0)(5.196;120)}
\rput(-5.196,0){\psline(0;0)(1.732;120)}
\rput(-1.732,0){\psline(0;0)(6.928;300)}
\rput(-3.464,0){\psline(0;0)(6.928;300)}
\rput(-5.196,0){\psline(0;0)(6.928;300)}
\rput(-6.062,-1.5){\psline(0;0)(5.196;300)}
\rput(-6.062,-4.5){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;300)}
\rput(3.464,0){\psline(0;0)(5.196;300)}
\rput(5.196,0){\psline(0;0)(1.732;300)}
\rput(1.732,0){\psline(0;0)(6.928;120)}
\rput(3.464,0){\psline(0;0)(6.928;120)}
\rput(5.196,0){\psline(0;0)(6.928;120)}
\rput(6.062,1.5){\psline(0;0)(5.196;120)}
\rput(6.062,4.5){\psline(0;0)(1.732;120)}

\rput(0,1){\psline(0;0)(7;150)}
\rput(0,1){\psline(0;0)(7;330)}
\rput(0,2){\psline(0;0)(7;150)}
\rput(0,2){\psline(0;0)(7;330)}
\rput(0,3){\psline(0;0)(6;150)}
\rput(0,3){\psline(0;0)(7;330)}
\rput(0,4){\psline(0;0)(4;150)}
\rput(0,4){\psline(0;0)(7;330)}
\rput(0,5){\psline(0;0)(7;330)}
\rput(0,6){\psline(0;0)(7;330)}
\rput(-1.732,6){\psline(0;0)(2;330)}

\rput(0,-1){\psline(0;0)(7;150)}
\rput(0,-1){\psline(0;0)(7;330)}
\rput(0,-2){\psline(0;0)(7;150)}
\rput(0,-2){\psline(0;0)(7;330)}
\rput(0,-3){\psline(0;0)(7;150)}
\rput(0,-3){\psline(0;0)(6;330)}
\rput(0,-4){\psline(0;0)(7;150)}
\rput(0,-4){\psline(0;0)(4;330)}
\rput(0,-5){\psline(0;0)(7;150)}
\rput(0,-5){\psline(0;0)(2;330)}
\rput(0,-6){\psline(0;0)(7;150)}

\rput(6.062,3.5){\psline(0;0)(5;150)}
\rput(6.062,4.5){\psline(0;0)(3;150)}
\rput(6.062,5.5){\psline(0;0)(1;150)}

\rput(-6.062,-3.5){\psline(0;0)(5;330)}
\rput(-6.062,-4.5){\psline(0;0)(3;330)}
\rput(-6.062,-5.5){\psline(0;0)(1;330)}

\psline(0;0)(7;330)
\psline(0;0)(7;150)
\psline(0;0)(7;210)
\psline(0;0)(6.928;240)

\pspolygon[fillcolor=gray,fillstyle=solid](0,0)(0,1)(0.433,0.75)

\psline[linewidth=1mm](0,1)(0,1.5)
\psline[linewidth=1mm](0,1)(.433,.75)
\psline[linewidth=1mm](0,0)(.866,1.5)
\psline[linewidth=1mm](-.866,1.5)(0,1)
\psline[linewidth=1mm](0,1)(0,0)
\psline[linewidth=1mm](-.433,.75)(-.866,1.5)

\psline[linewidth=1mm](0,1.5)(0,3)
\psline[linewidth=1mm](0,3)(-1.732,6)
\psline[linewidth=1mm](-.866,1.5)(-3.464,6)

\psline[linewidth=1mm](.433,.75)(1.732,0)
\psline[linewidth=1mm](1.732,0)(6.062,0)
\psline[linewidth=1mm](2.598,1.5)(6.062,1.5)

\psline[linewidth=1mm](-.433,.75)(-1.732,0)
\psline[linewidth=1mm](-1.732,0)(-6.062,0)
\psline[linewidth=1mm](-2.598,1.5)(-6.062,1.5)

\psline[linewidth=1mm](.866,0)(.866,-1.5)
\psline[linewidth=1mm](.866,-1.5)(3.464,-6)
\psline[linewidth=1mm](.866,0)(1.732,0)
\psline[linewidth=1mm](2.598,-1.5)(5.196,-6)

\psline[linewidth=1mm](-.866,0)(-.866,-1.5)
\psline[linewidth=1mm](-.866,-1.5)(-3.464,-6)
\psline[linewidth=1mm](-.866,0)(-1.732,0)
\psline[linewidth=1mm](-2.598,-1.5)(-5.196,-6)

\psline[linewidth=1mm](.433,2.25)(0,3)
\psline[linewidth=1mm](0.866,4.5)(1.732,6)
\psline[linewidth=1mm](.433,2.25)(1.732,3)
\psline[linewidth=1mm](1.732,3)(3.464,6)

\psline[linewidth=1mm](0,0)(0,-6)
\psline[linewidth=1mm](.433,-.75)(.866,-1.5)
\psline[linewidth=1mm](.866,-1.5)(.866,-6)

\psline[linewidth=1mm](1.732,0)(6.062,-2.5)
\psline[linewidth=1mm](2.598,-1.5)(6.062,-3.5)

\psline[linewidth=1mm](-1.732,0)(-6.062,-2.5)
\psline[linewidth=1mm](-2.598,-1.5)(-6.062,-3.5)

\psline[linewidth=1mm](.866,1.5)(6.062,4.5)
\psline[linewidth=1mm](2.598,1.5)(6.062,3.5)

\psline[linewidth=1mm](-.866,1.5)(-6.062,4.5)
\psline[linewidth=1mm](-2.598,1.5)(-6.062,3.5)

\psline[linewidth=1mm](0,3)(0,6)
\psline[linewidth=1mm](.866,4.5)(.866,6)

\psline[linewidth=1mm](.866,1.5)(1.732,3)
\psline[linewidth=1mm](0,0)(-.866,-1.5)

\psline[linewidth=1mm](-.866,.5)(-2.598,1.5)
\psline[linewidth=1mm](.866,.5)(2.598,1.5)
\psline[linewidth=1mm](.866,2.5)(.866,4.5)
\psline[linewidth=1mm](.866,-.5)(2.598,-1.5)
\psline[linewidth=1mm](-.866,-.5)(-2.598,-1.5)

\psline[linewidth=1mm](0,-1)(.433,-.75)

\psline[linewidth=1mm](0,0)(.866,.5)
\psline[linewidth=1mm](0,0)(-.866,-.5)
\psline[linewidth=1mm](0.866,1.5)(.866,2.5)

\rput(-1.5,-4.33){{\small ${\bf \tilde{c}_{0}^{1}}$}}
\rput(1.988,-4.31){{\small ${\bf \tilde{c}_{0}^{2}}$}}
\rput(5.452,-4.31){{\small ${\bf \tilde{c}_{0}^{3}}$}}
\rput(5.452,-1.31){{\small ${\bf \tilde{c}_{0}^{4}}$}}
\rput(3.69,1.7){{\small ${\bf \tilde{c}_{0}^{5}}$}}
\rput(2.824,3.2){{\small ${\bf \tilde{c}_{0}^{6}}$}}
\rput(1.1,5.75){{\small ${\bf \tilde{c}_{0}^{7}}$}}
\rput(-0.23,4.67){{\small ${\bf \tilde{c}_{0}^{8}}$}}
\rput(-2.372,3.2){{\small ${\bf \tilde{c}_{0}^{9}}$}}
\rput(-4.97,1.7){{\small ${\bf \tilde{c}_{0}^{10}}$}}

\rput(-4.97,-1.3){{\small ${\bf \tilde{c}_{0}^{11}}$}}
\rput(-4.97,-4.3){{\small ${\bf \tilde{c}_{0}^{12}}$}}

\rput(-0.66,-.63){{\footnotesize ${\bf  \tilde{c}_{3}^{1}}$}}
\rput(1.12,2.33){{\footnotesize ${\bf \tilde{c}_{3}^{2}}$}}

\rput(2.3,-2.33){{\small ${\bf  \tilde{c}_{1}^{1}}$}}
\rput(3.2,.73){{\small ${\bf \tilde{c}_{1}^{2}}$}}
\rput(1.5,4.34){{\small ${\bf \tilde{c}_{1}^{3}}$}}
\rput(-1.5,4.34){{\small ${\bf \tilde{c}_{1}^{4}}$}}
\rput(-3.2,.73){{\small ${\bf \tilde{c}_{1}^{5}}$}}
\rput(-2.3,-2.33){{\small ${\bf  \tilde{c}_{1}^{6}}$}}

\rput(0.3,-4.33){{\small ${\bf  \tilde{c}_{2}^{1}}$}}
\rput(3.2,-1.33){{\small ${\bf \tilde{c}_{2}^{2}}$}}
\rput(3.2,2.34){{\small ${\bf \tilde{c}_{2}^{3}}$}}
\rput(0.3,4.33){{\small ${\bf \tilde{c}_{2}^{4}}$}}
\rput(-3.4,2.34){{\small ${\bf \tilde{c}_{2}^{5}}$}}
\rput(-3.2,-1.33){{\small ${\bf \tilde{c}_{2}^{6}}$}}

\rput(.4,-.43){{\small ${\bf \tilde{c}_{4}^{1}}$}}
\rput(.4,1.43){{\small ${\bf \tilde{c}_{4}^{2}}$}}
\rput(-.4,.43){{\small ${\bf \tilde{c}_{4}^{3}}$}}

\rput(.4,.43){{\tiny ${\bf \tilde{c}_{4}^{3}}$}}

\rput(.17,.68){{\small ${\bf \tilde{c}_{6}^{1}}$}}

\rput(0,-7){\textsc{Figure 14}. Partition of $\tilde{G}_{2}$ into cells}

\end{pspicture}
\end{center}

\newpage

The green edges only hold for $1/2\leq r<1$.

\begin{center}
\begin{pspicture}(-1.3,-1.5)(13,13)
\psset{unit=.7pt}

\pscircle(-100,0){10}
\rput(-100,0){{\small $u_{0}^{1}$}}
\pscircle(-60,0){10}
\rput(-60,0){{\small $u_{0}^{2}$}}

\pscircle(0,0){10}
\rput(0,0){{\small $u_{0}^{3}$}}
\pscircle(40,0){10}
\rput(40,0){{\small $u_{0}^{4}$}}
\pscircle(100,0){10}
\rput(100,0){{\small $u_{0}^{5}$}}
\pscircle(140,0){10}
\rput(140,0){{\small $u_{0}^{6}$}}

\pscircle(200,0){10}
\rput(200,0){{\small $u_{0}^{7}$}}
\pscircle(240,0){10}
\rput(240,0){{\small $u_{0}^{8}$}}

\pscircle(300,0){10}
\rput(300,0){{\small $u_{0}^{9}$}}
\pscircle(340,0){10}
\rput(340,0){{\small $u_{0}^{10}$}}

\pscircle(400,0){10}
\rput(400,0){{\small $u_{0}^{11}$}}
\pscircle(440,0){10}
\rput(440,0){{\small $u_{0}^{12}$}}

\pscircle(500,0){10}
\rput(500,0){{\small $u_{0}^{1}$}}
\pscircle(540,0){10}
\rput(540,0){{\small $u_{0}^{2}$}}

\pscircle(20,100){10}
\rput(20,100){{\small $u_{1}^{1}$}}

\pscircle(120,100){10}
\rput(120,100){{\small $u_{1}^{2}$}}

\pscircle(220,100){10}
\rput(220,100){{\small $u_{1}^{3}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](270,100){10}
\rput(270,100){{\small $u_{1}^{4}$}}

\pscircle(320,100){10}
\rput(320,100){{\small $u_{1}^{5}$}}

\pscircle(420,100){10}
\rput(420,100){{\small $u_{1}^{6}$}}

\pscircle(-80,200){10}
\rput(-80,200){{\small $u_{2}^{1}$}}

\pscircle(20,200){10}
\rput(20,200){{\small $u_{2}^{2}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](120,200){10}
\rput(120,200){{\small $u_{2}^{3}$}}

\pscircle(220,200){10}
\rput(220,200){{\small $u_{2}^{4}$}}

\pscircle(320,200){10}
\rput(320,200){{\small $u_{2}^{5}$}}

\pscircle(420,200){10}
\rput(420,200){{\small $u_{2}^{6}$}}

\pscircle(70,300){10}
\rput(70,300){{\small $u_{4}^{1}$}}

\pscircle(245,300){10}
\rput(245,300){{\small $u_{4}^{2}$}}

\pscircle(370,300){10}
\rput(370,300){{\small $u_{4}^{3}$}}

\pscircle(70,340){10}
\rput(70,340){{\small $u_{5}^{1}$}}

\pscircle(270,240){10}
\rput(270,240){{\small $u_{3}^{2}$}}

\pscircle(370,240){10}
\rput(370,240){{\small $u_{3}^{1}$}}

\pscircle(307.5,450){10}
\rput(307.5,450){{\small $u_{6}^{1}$}}

\psline(20,90)(-60,10)

\psline(20,90)(40,10)

\psline[linecolor=green](20,90)(-100,10)

\psline(120,90)(0,10)

\psline(120,90)(140,10)

\psline(220,90)(100,10)

\psline(220,90)(240,10)

\psline[linecolor=green](220,90)(300,10)

\psline(270,90)(200,10)

\psline(270,90)(300,10)

\psline(320,90)(340,10)

\psline(320,90)(400,10)

\psline(420,90)(440,10)

\psline(420,90)(500,10)

\psline(-80,190)(-100,10)

\psline(-80,190)(-60,10)

\psline(-80,190)(20,110)

\psline(-80,190)(120,110)

\psline(20,190)(20,110)

\psline(20,190)(120,110)

\psline(20,190)(-100,10)

\psline(120,190)(120,110)

\psline(120,190)(90,110)(100,10)

\psline(220,190)(270,110)

\psline(220,190)(120,110)

\psline(220,190)(220,110)

\psline(320,190)(320,110)

\psline(320,190)(270,110)

\psline(320,190)(370,100)(500,10)

\psline(420,190)(420,110)

\psline(420,190)(320,110)

\psline(420,190)(270,110)

\psline(70,290)(-80,210)

\psline(70,290)(20,210)

\psline(245,290)(120,210)

\psline(245,290)(220,210)

\psline(245,290)(270,250)

\psline(370,290)(370,250)

\psline(370,290)(320,210)

\psline(370,230)(420,110)

\psline(370,290)(420,210)

\psline(270,230)(220,110)

\psline[linecolor=green](270,230)(270,110)

\psline(70,330)(70,310)

\psline(307.5,440)(245,310)

\psline(307.5,440)(370,310)

\psline(307.5,440)(70,350)

\rput(200,-50){Figure 15. Order $\preceq$ on $U$}

\end{pspicture}
\end{center}

Let $w=s_{1}s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1}s_{2}$, and $w_{1}=s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}$. In the following table we have
$$y\in \{zw^{n}| z\in Y(w), n\in\mathbb{N}\} \text{ and } y_{1}\in \{yw_{1}^{n}| y\in Y(w_{1}), n\in\mathbb{N}\} $$

\newpage

\newpage

\vspace{2cm}
{\small
\begin{table}[htbp] \caption{Condition {\bf I5} for $0<r<1$}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{1}^{3} & s_{2}s_{1}s_{2}s_{1} & T_{xu} + v^{a}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{3}s_{2}s_{1}s_{2}s_{1} & T_{xu} + v^{a}T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & y_{1}w_{1} &
T_{xu} + v^{a}T_{y_{1}s_{2}s_{3}}C_{u_{0}^{6}}+T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline

u_{1}^{3} & s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{2}s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline
u_{1}^{3} & y_{1}w_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{y_{1}s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}+v^{a}T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{6}}\\\hline

u_{1}^{6} & s_{2}s_{1}s_{2}s_{1} & T_{xu} + v^{a}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{3}s_{2}s_{1}s_{2}s_{1} & T_{xu} + v^{a}T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & y_{1}w_{1} &
T_{xu} + v^{a}T_{y_{1}s_{2}s_{3}}C_{u_{0}^{1}}+T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{1}^{6} & s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{1}s_{3}s_{2}s_{1} & T_{xu} +T_{s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & s_{3}s_{2}s_{1}s_{2}s_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{1}^{6} & y_{1}w_{1}s_{3}s_{2}s_{1} &
T_{xu} +T_{y_{1}s_{2}s_{3}s_{2}s_{1}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}+v^{a}T_{y_{1}s_{3}s_{2}s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

u_{2}^{4} & s_{2}s_{1}s_{2} & T_{xu} +C_{u_{0}^{6}}\\\hline
u_{2}^{4} & s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{4} & s_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{a}T_{s_{3}}C_{u_{0}^{6}}\\\hline
u_{2}^{4} & ys_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{a}T_{ys_{3}}C_{u_{0}^{6}}\\\hline

u_{2}^{6} & s_{2}s_{1}s_{2} & T_{xu} +C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{3}s_{2}s_{1}s_{2} & T_{xu} +T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & s_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{a}T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{6} & ys_{1}s_{3}s_{2}s_{1}s_{2} & T_{xu} +v^{a}T_{ys_{3}}C_{u_{0}^{1}}\\\hline

 \end{array}$
\end{center}
\end{table}}

\end{longlist}
\newpage

\section{Partition of the affine Weyl group $\tilde{B}_{2}$ into cells}
\label{sec3}

\newcounter{b}
\setcounter{b}{16}

Let $(W,S)$ be the affine Weyl group of type $\tilde{B}_{2}$ with diagram and weight function given by
\begin{center}
\begin{picture}(150,32)
\put( 40, 10){\circle{10}}
\put( 44.5,  8){\line(1,0){31.75}}
\put( 44.5,  12){\line(1,0){31.75}}
\put( 81, 10){\circle{10}}
\put( 85.5,  8){\line(1,0){29.75}}
\put( 85.5,  12){\line(1,0){29.75}}
\put(120, 10){\circle{10}}
\put( 38, 20){$a$}
\put( 78, 20){$b$}
\put(118, 20){$c$}
\put( 38, -3){$s_{1}$}
\put( 78, -3){$s_{2}$}
\put(118,-3){$s_{3}$}
\end{picture}
\end{center}
where $a,b,c$ are positive integers. The partition of $W$ into cells only depend on the ratios $r_{1}=a/b$ and $r_{2}=c/b$. Note that by symmetry of diagram we may assume that $a\geq c$, that is $r_{1}\geq r_{2}$. We define the following open subsets of $\mathbb{R}^{2}$:
\begin{center}
\psset{xunit=1.5cm}
\psset{yunit=1.5cm}
\begin{pspicture}(0,-0.3)(5.5,5.3)
\psgrid[subgriddiv=1,griddots=10,gridlabels=8 pt](0,0)(5,5)

\psline(0,0)(5,5)
\psline(1,0)(1,1)
\psline(1,1)(5,1)
\psline(1,0)(0.5,.5)
\psline(1,0)(5,4)
\psline(2,0)(1,1)
\psline(2,0)(5,3)

\psline(0,1)(1,1)

\psline(.5,.5)(0,1)

\psline(1,1)(1,5)

\psline(1,1)(0,2)

\psline(0,2)(3,5)
\psline(0,1)(4,5)

\rput(3.5,.5){$A_{1}$}
\rput(2,.5){$A_{2}$}
\rput(1.5,.2){$A_{3}$}
\rput(1.2,.5){$A_{4}$}
\rput(1.5,.8){$A_{5}$}

\rput(4.5,1.5){$C_{3}$}
\rput(3,1.5){$C_{2}$}
\rput(2,1.5){$C_{1}$}

\rput(.5,.25){$B_{2}$}
\rput(.8,.5){$B_{1}$}

\psline{->}(0,0)(0,5)
\psline{->}(0,0)(5,0)
\end{pspicture}
\end{center}

\begin{Rem}
Let $V$ be an Euclidean space of dimension 3 with standard basis $v_{1},v_{2},v_{3}$ corresponding respectively to the conjugacy classes $\{s_{1}\}$, $\{s_{2}\}$ and $\{s_{3}\}$ in $S$.  In \cite{jeju4} we claimed that the essential hyperplanes of $W$ were
$$\mathcal{H}_{(1,0,0)},\mathcal{H}_{(0,1,0)},\mathcal{H}_{(0,0,1)},\mathcal{H}_{(\epsilon,\epsilon,0)},\mathcal{H}_{(0,\epsilon,\epsilon)},\mathcal{H}_{(\epsilon,0,\epsilon)},\mathcal{H}_{(\epsilon,\epsilon,\epsilon)},\mathcal{H}_{(\epsilon,2\epsilon,\epsilon)}$$
where $\epsilon=\pm 1$. The picture above is just the projection of this hyperplane arrangement on the hyperplane $y=1$.
\end{Rem}

\newpage

\subsection{Partitions of $W$}
We describe the partitions $\mathcal{P}_{\mathcal{LR},\mathfrak{C}}$ and $\mathcal{P}_{\mathfrak{C}}$ of $\mathfrak{C}$ and the corresponding partition of $W$ according to \cite[Conjecture 3.3]{jeju4}. We keep the notation of  \cite[\S 5]{jeju4}.

\vspace{.5cm}

\begin{longlist}

\item Case $r_{1}=r_{2}, r_{2}>1$ \\

{\small
\begin{table}[htpb] \caption{Partition $\mathcal{P}_{LR,\mathfrak{C}}$ and values of the $\mathbf{a}$-function}
\label{PlrcG}
\begin{center}
$\renewcommand{\arraystretch}{1.4}
\begin{array}{|l|c|} \hline
b_{8}=\{e\} & 0 \\
b_{7}=\{s_{2}\} & b\\
b_{6}=\{s_{1},s_{1}s_{2}, s_{2}s_{1},s_{2}s_{1}s_{2}\}&  a\\
b_{5}=\{s_{3}, s_{3}s_{2}, s_{2}s_{3}, s_{2}s_{3}s_{2}\}&  a\\
b_{4}=\{s_{3}s_{2}s_{3}\} & 2a-b \\
b_{3}=\{s_{1}s_{2}s_{1}\}& 2a-b\\
b_{2}=\{s_{1}s_{3}\}&  2a\\
b_{1}= \{w_{2,3}\} & 2a+2b\\
b_{0}= \{w_{1,2}\} & 2a+2b\\ \hline
\end{array}$
\end{center}
\end{table}
}

{\small
\begin{table}[h] \caption{Partition $\mathcal{P}_{\mathfrak{C}}$}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|ccccccc|} \hline
r_{2}>1 & b_{0}\cup b_{1} & b_{2} & b_{3} & b_{4}  & b_{5}\cup b_{6} & b_{7} & b_{8}\\ \hline
 \end{array}$
\end{center}
\end{table}}

\psset{linewidth=.03mm}
\psset{unit=.5cm}

\begin{textblock}{10}(5.775,15.5)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,6)(5,6)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-6,6)(-5,6)(-.5,1.5)%

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-.5,1.5)(-1,1)(-.5,.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(.5,1.5)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=BurntOrange](0,0)(0,1)(-.5,.5)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=Aquamarine](0,0)(0,-1)(0.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$r_{1}=r_{2}, r_{2}>1$}

\end{pspicture}
\end{center}

\end{textblock}

$\ $\\
\newpage

\item Case $r_{1}>1$ and $r_{2}>1$ \\

{\small
\begin{table}[h] \caption{Partition $\mathcal{P}_{LR,\mathfrak{C}}$ and values of the $\mathbf{a}$-function}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|l|c|} \hline
b_{8}=\{e\} & 0\\
b_{7}=\{s_{2}\} & b\\
b_{6}=\{s_{3},s_{2}s_{3},s_{3}s_{2},s_{2}s_{3}s_{2}\}   & c\\
b_{5}=\{s_{3}s_{2}s_{3}\} & 2c-b\\
b_{4}=\{s_{2}s_{3}s_{2}s_{3}\} & 2b+2c\\
b_{3}=\{s_{1},s_{2}s_{1},s_{1}s_{2},s_{2}s_{1}s_{2}\} & a\\
b_{2}=\{s_{1}s_{3}\}& a+c\\
b_{1}=\{s_{1}s_{2}s_{1}\} & 2a-b\\
b_{0}=\{w_{1,2}\}&  2a+2b\\ \hline
 \end{array}$
\end{center}
\end{table}}

{\small
\begin{table}[h] \caption{Partition $\mathcal{P}_{\mathfrak{C}}$}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|ccccccccc|} \hline
(r_{1},r_{2})\in C_{3}  & b_{0} & b_{1} & b_{2} &\multicolumn{2}{r}{ b_{3}  \leftrightarrow b_{4}} & b_{5} & b_{6} & b_{7} & b_{8}\\ \hline
r_{1}-r_{2}-2=0  & b_{0} & b_{1} &\multicolumn{2}{r}{ b_{2} \cup b_{4}}  & b_{3} & b_{5} & b_{6} & b_{7} & b_{8}\\ \hline
(r_{1},r_{2})\in C_{2}  &b_{0} & \multicolumn{2}{r}{ b_{1}  \leftrightarrow b_{4}}& b_{2} & b_{3} & b_{5} & b_{6} & b_{7} & b_{8}\\ \hline
r_{1}-r_{2}-1=0  & b_{0} & b_{4} &\multicolumn{2}{r}{ b_{1} \cup b_{2}}  & b_{3} & b_{5} & b_{6} & b_{7} & b_{8}\\ \hline
(r_{1},r_{2})\in C_{1}  &b_{0} &  b_{4}  & b_{2} & b_{1} & b_{3} & b_{5} & b_{6} & b_{7} & b_{8}\\ \hline
\end{array}$
\end{center}
\end{table}}

\psset{linewidth=.13mm}

\begin{textblock}{10}(2,17)
\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0.5,0.5)(1,1)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,0.5)(-1,1)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0.5,1.5)(5,6)(4,6)(0,2)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(-0,2)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,6)(5,6)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-6,6)(-5,6)(-.5,1.5)%

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(-.5,1.5)(-1,1)(-.5,.5)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=BurntOrange](0,0)(0,1)(-.5,.5)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=green!30!black!100!](0,1)(-.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(6,1)(6,0)(2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,1)(-6,1)(-6,0)(-2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,2)(0,6)(1,6)(1,3)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$(r_{1},r_{2}) \in C_{3}$}
\end{pspicture}
\end{center}\end{textblock}

\begin{textblock}{10}(9.55,17)
\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0.5,0.5)(1,1)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,0.5)(-1,1)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0.5,1.5)(5,6)(4,6)(0,2)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(-0,2)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,6)(5,6)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-6,6)(-5,6)(-.5,1.5)%

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(-.5,1.5)(-1,1)(-.5,.5)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=BurntOrange](0,0)(0,1)(-.5,.5)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0,1)(-.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(6,1)(6,0)(2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,1)(-6,1)(-6,0)(-2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,2)(0,6)(1,6)(1,3)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$r_{1}-r_{2}-2=0$}

\end{pspicture}
\end{center}

\end{textblock}

$\ $\\
\newpage

\begin{textblock}{10}(2,3)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=BlueGreen](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=BlueGreen](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=BlueGreen](.5,1.5)(0,2)(1,3)(1,2)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,6)(5,6)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-6,6)(-5,6)(-.5,1.5)%

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(-.5,1.5)(-1,1)(-.5,.5)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=BurntOrange](0,0)(0,1)(-.5,.5)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(6,1)(6,0)(2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,1)(-6,1)(-6,0)(-2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,2)(0,6)(1,6)(1,3)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$(r_{1},r_{2}) \in C_{2}$}

\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(9.55,3)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,6)(5,6)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-6,6)(-5,6)(-.5,1.5)%

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(-.5,1.5)(-1,1)(-.5,.5)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=BurntOrange](0,0)(0,1)(-.5,.5)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-1)(0.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$r_{1}-r_{2}-1=0$}

\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(5.5,10)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,6)(5,6)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-6,6)(-5,6)(-.5,1.5)%

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(-.5,1.5)(-1,1)(-.5,.5)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=BurntOrange](0,0)(0,1)(-.5,.5)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=Aquamarine](0,0)(0,-1)(0.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$(r_{1},r_{2}) \in C_{1}$}

\end{pspicture}
\end{center}

\end{textblock}

\vspace*{13.5cm}

\item Case $r_{1}>1$ and $r_{2}=1$\\
{\small
\begin{table}[h] \caption{Partition $\mathcal{P}_{LR,\mathfrak{C}}$ and values of the $\mathbf{a}$-function}
\label{PlrcG}
\begin{center}
$\renewcommand{\arraystretch}{1.4}
\begin{array}{|l|c|} \hline
b_{6}=\{e\} & 0 \\
b_{5}=\{s_{2},s_{3},s_{3}s_{2},s_{2}s_{3},s_{3}s_{2}s_{3},s_{2}s_{3}s_{2}\} & b\\
b_{4}=\{s_{2}s_{3}s_{2}s_{3}\}& 4b\\
b_{3}=\{s_{1},s_{2}s_{1},s_{1}s_{2},s_{2}s_{1}s_{2}\}& a \\
b_{2}=\{s_{1}s_{3}\}&  a+b\\
b_{1}= \{s_{1}s_{2}s_{1}\} & 2a-b\\
b_{0}= \{w_{1,2}\} & 2a+2b\\ \hline
\end{array}$
\end{center}
\end{table}
}

\newpage

{\small
\begin{table}[h] \caption{Partition $\mathcal{P}_{\mathfrak{C}}$}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|ccccccc|} \hline
r_{1}>3 & b_{0} & b_{1} & b_{2} &  \multicolumn{2}{r}{b_{3} \leftrightarrow b_{4}} & b_{5} & b_{6}\\ \hline

r_{1}=3 &b_{0} & b_{1} & \multicolumn{2}{r}{b_{2}\cup b_{4} }& b_{3} & b_{5} & b_{6}\\ \hline

3>r_{1}>2 &b_{0} & \multicolumn{2}{r}{b_{1} \leftrightarrow b_{4}} & b_{2}  & b_{3} & b_{5} & b_{6}\\ \hline

r_{1}=2 &b_{0} & b_{4} & \multicolumn{2}{r}{b_{1} \cup  b_{2}} & b_{3}  & b_{5} & b_{6}\\ \hline

2>r_{1}>1 &b_{0} & b_{4} & b_{2} &  b_{1} & b_{3}  & b_{5} & b_{6}\\ \hline

 \end{array}$
\end{center}
\end{table}}

\psset{linewidth=.13mm}

\begin{textblock}{10}(2,7.2)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0.5,0.5)(1,1)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,0.5)(-1,1)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0.5,1.5)(5,6)(4,6)(0,2)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(-0,2)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,6)(5,6)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-6,6)(-5,6)(-.5,1.5)%

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(-.5,1.5)(-1,1)(-.5,.5)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(0,1)(-.5,.5)

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=green!30!black!100!](0,1)(-.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(6,1)(6,0)(2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,1)(-6,1)(-6,0)(-2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,2)(0,6)(1,6)(1,3)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$r_{1}>3$}

\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(9.55,7.2)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0.5,0.5)(1,1)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,0.5)(-1,1)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0.5,1.5)(5,6)(4,6)(0,2)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(-0,2)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,6)(5,6)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-6,6)(-5,6)(-.5,1.5)%

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(-.5,1.5)(-1,1)(-.5,.5)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(0,1)(-.5,.5)

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0,1)(-.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(6,1)(6,0)(2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,1)(-6,1)(-6,0)(-2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,2)(0,6)(1,6)(1,3)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$r_{1}=3$}

\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(2,14)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=BlueGreen](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=BlueGreen](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=BlueGreen](.5,1.5)(0,2)(1,3)(1,2)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,6)(5,6)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-6,6)(-5,6)(-.5,1.5)%

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(-.5,1.5)(-1,1)(-.5,.5)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(0,1)(-.5,.5)

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(6,1)(6,0)(2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,1)(-6,1)(-6,0)(-2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,2)(0,6)(1,6)(1,3)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$3>r_{1}>2$}

\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(9.55,14)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,1.5)(0,2)(1,3)(1,2)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,6)(5,6)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-6,6)(-5,6)(-.5,1.5)%

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(-.5,1.5)(-1,1)(-.5,.5)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(0,1)(-.5,.5)

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(6,1)(6,0)(2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,1)(-6,1)(-6,0)(-2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,2)(0,6)(1,6)(1,3)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$r_{1}=2$}

\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(5.5,20.7)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,6)(5,6)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-6,6)(-5,6)(-.5,1.5)%

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(-.5,1.5)(-1,1)(-.5,.5)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(0,1)(-.5,.5)

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=Aquamarine](0,0)(0,-1)(0.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$2>r_{1}>1$}

\end{pspicture}
\end{center}

\end{textblock}

\newpage
\item Case $ r_{1}>1, r_{2}<1$ \\

{\small
\begin{table}[h!] \caption{Partition $\mathcal{P}_{LR,\mathfrak{C}}$ and values of the $\mathbf{a}$-function}
\label{PlrcG}
\begin{center}
$\renewcommand{\arraystretch}{1.4}
\begin{array}{|l|c|} \hline
b_{8}=\{e\} & 0 \\
b_{7}=\{s_{3}\} & c\\
b_{6}=\{s_{2},s_{3}s_{2},s_{2}s_{3},s_{3}s_{2}s_{3}\}& b\\
b_{5}=\{s_{2}s_{3}s_{2}\} & 2b-c\\
b_{4}=\{s_{2}s_{3}s_{2}s_{3}\}& 2b+2c\\
b_{3}=\{s_{1},s_{2}s_{1},s_{1}s_{2},s_{2}s_{1}s_{2}\}& a \\
b_{2}=\{s_{1}s_{3}\}&  a+c\\
b_{1}= \{s_{1}s_{2}s_{1}\} & 2a-b\\
b_{0}= \{w_{1,2}\} & 2a+2b\\ \hline
\end{array}$
\end{center}
\end{table}
}

{\small
\begin{table}[h] \caption{Partition $\mathcal{P}_{\mathfrak{C}}$}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|ccccccccc|} \hline
(r_{1},r_{2})\in A_{1}  & b_{0} & b_{1} & b_{2} &\multicolumn{2}{r}{ b_{3}  \leftrightarrow b_{4}} & b_{5} & b_{6} & b_{7} & b_{8}\\ \hline
r_{1}-r_{2}-2=0  & b_{0} & b_{1} &\multicolumn{2}{r}{ b_{2} \cup b_{4}}  & b_{3} & b_{5} & b_{6} & b_{7} & b_{8}\\ \hline
(r_{1},r_{2})\in A_{2}  &b_{0} & b_{1} & b_{4} & b_{2} & b_{3} & b_{5} & b_{6} & b_{7} & b_{8}\\ \hline
r_{1}+r_{2}-2=0, r_{1}-r_{2}>1 &b_{0} & b_{1} & b_{4} & b_{2} &\multicolumn{2}{r}{ b_{3} \cup b_{5}} & b_{6} & b_{7} & b_{8}\\ \hline
(r_{1},r_{2})\in A_{3} & b_{0} & \multicolumn{2}{r}{  b_{1} \leftrightarrow b_{4}}  & b_{2}  & b_{5} & b_{3} & b_{6} & b_{7} & b_{8} \\ \hline
r_{1}-r_{2}-1=0, r_{1}+r_{2}<2  & b_{0} &  b_{4} &  \multicolumn{2}{r}{b_{1} \cup b_{2}}  & b_{5} & b_{3} & b_{6} & b_{7} & b_{8} \\ \hline

(r_{1},r_{2})\in A_{4} & b_{0} & b_{4} & b_{2} & b_{1}  & b_{5} & b_{3} & b_{6} & b_{7} & b_{8} \\ \hline
r_{1}+r_{2}-2=0, r_{1}-r_{2}<1 & b_{0} & b_{4} & b_{2} & b_{1}  &\multicolumn{2}{r}{ b_{5} \cup b_{3}} & b_{6} & b_{7} & b_{8} \\ \hline
(r_{1},r_{2})\in A_{5} & b_{0} & b_{4} & b_{2} & b_{1} & b_{3} & b_{5} & b_{6} & b_{7} & b_{8} \\ \hline
r_{1}-r_{2}-1=0, r_{1}+r_{2}>2& b_{0} & b_{4} & \multicolumn{2}{r}{ b_{1} \cup b_{2}} & b_{3} & b_{5} & b_{6} & b_{7} & b_{8} \\ \hline
(r_{1},r_{2})=(3/2,1/2)  & b_{0} & b_{4} &\multicolumn{2}{r}{b_{1} \cup b_{2}} & \multicolumn{2}{r}{ b_{3} \cup b_{5}}& b_{6} & b_{7} & b_{8} \\ \hline
\end{array}$
\end{center}
\end{table}}

\psset{linewidth=.13mm}

\begin{textblock}{10}(2,19.5)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(.5,1.5)(1,2)(2,2)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(1,0)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-1,0)(-1,-1)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(1,1)
\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-1)(.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=BurntOrange](0,1)(-1,1)(-.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=green!30!black!100!](0,1)(0,2)(-.5,1.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](.5,1.5)(0,2)(1,3)(1,2)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$(r_{1},r_{2}) \in A_{1}$}
\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(9.55,19.5)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(.5,1.5)(1,2)(2,2)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(1,0)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-1,0)(-1,-1)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(1,1)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-1)(.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=BurntOrange](0,1)(-1,1)(-.5,1.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](.5,1.5)(0,2)(1,3)(1,2)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)
\rput(0,-6.7){$r_{1}-r_{2}-2=0$}
\end{pspicture}
\end{center}

\end{textblock}

$\ $\\

\newpage

\pagestyle{empty}

\begin{textblock}{10}(2,.5)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(.5,1.5)(1,2)(2,2)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(1,0)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-1,0)(-1,-1)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(1,1)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-1)(.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=BurntOrange](0,1)(-1,1)(-.5,1.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\pspolygon[fillstyle=solid,fillcolor=BlueGreen](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=BlueGreen](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=BlueGreen](.5,1.5)(0,2)(1,3)(1,2)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)
\rput(0,-6.7){$(r_{1},r_{2}) \in A_{2}$}
\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(9.55,.5)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(.5,1.5)(1,2)(2,2)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(1,0)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-1,0)(-1,-1)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(1,1)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-1)(.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\pspolygon[fillstyle=solid,fillcolor=BlueGreen](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=BlueGreen](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=BlueGreen](.5,1.5)(0,2)(1,3)(1,2)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)
\rput(0,-6.7){$r_{1}+r_{2}-2=0, r_{1}-r_{2}>1$}
\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(2,7.3)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=Cerulean](1,1)(.5,1.5)(1,2)(2,2)
\pspolygon[fillstyle=solid,fillcolor=Cerulean](0,0)(.5,.5)(1,0)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=Cerulean](0,0)(-.5,.5)(-1,0)(-1,-1)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(1,1)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-1)(.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\pspolygon[fillstyle=solid,fillcolor=BlueGreen](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=BlueGreen](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=BlueGreen](.5,1.5)(0,2)(1,3)(1,2)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)
\rput(0,-6.7){$(r_{1},r_{2}) \in A_{3}$}
\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(9.55,7.3)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=Cerulean](1,1)(.5,1.5)(1,2)(2,2)
\pspolygon[fillstyle=solid,fillcolor=Cerulean](0,0)(.5,.5)(1,0)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=Cerulean](0,0)(-.5,.5)(-1,0)(-1,-1)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(1,1)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-1)(.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)
\rput(0,-6.7){$r_{1}+r_{2}-1=0, r_{1}+r_{2}>2$}
\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(2,14.2)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=Cerulean](1,1)(.5,1.5)(1,2)(2,2)
\pspolygon[fillstyle=solid,fillcolor=Cerulean](0,0)(.5,.5)(1,0)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=Cerulean](0,0)(-.5,.5)(-1,0)(-1,-1)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(1,1)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=Aquamarine](0,0)(0,-1)(.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)
\rput(0,-6.7){$(r_{1},r_{2}) \in A_{4}$}
\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(9.55,14.2)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,1.5)(0,2)(1,3)(1,2)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(.5,1.5)(5,6)(6,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-.5,1.5)(-5,6)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(1,1)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-.5,1.5)(-1,1)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(6,1)(6,0)(2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,1)(-6,1)(-6,0)(-2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,2)(0,6)(1,6)(1,3)

\pspolygon[fillstyle=solid,fillcolor=Aquamarine](0,0)(0,-1)(.5,-.5)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)
\rput(0,-6.7){$r_{1}+r_{2}-2=0, r_{1}-r_{2}<1$}
\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(2,21.1)
\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=gray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,1.5)(0,2)(1,3)(1,2)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(.5,1.5)(5,6)(6,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-.5,1.5)(-5,6)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(1,1)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=BurntOrange](0,1)(-.5,1.5)(-1,1)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(6,1)(6,0)(2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,1)(-6,1)(-6,0)(-2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,2)(0,6)(1,6)(1,3)

\pspolygon[fillstyle=solid,fillcolor=Aquamarine](0,0)(0,-1)(.5,-.5)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)
\rput(0,-6.7){$(r_{1},r_{2}) \in A_{5}$}
\end{pspicture}
\end{center}
\end{textblock}

\begin{textblock}{10}(9.55,21.1)
\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(.5,1.5)(1,2)(2,2)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(1,0)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-1,0)(-1,-1)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(1,1)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-1)(.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=BurntOrange](0,1)(-1,1)(-.5,1.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,1.5)(0,2)(1,3)(1,2)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)
\rput(0,-6.7){$r_{1}-r_{2}-1=0, r_{1}+r_{2}>2$}
\end{pspicture}
\end{center}
\end{textblock}

$\ $\\
\newpage

\begin{textblock}{10}(5.775,2)
\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(.5,1.5)(1,2)(2,2)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(1,0)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-1,0)(-1,-1)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(1,1)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-1)(.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,1.5)(0,2)(1,3)(1,2)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)
\rput(0,-6.7){$(r_{1},r_{2})=(3/2,1/2)$}
\end{pspicture}
\end{center}
\end{textblock}

\vspace*{7cm}

\item Case $ r_{1}=1, r_{2}<1$\\

{\small
\begin{table}[htpb] \caption{Partition $\mathcal{P}_{LR,\mathfrak{C}}$ and values of the $\mathbf{a}$-function}
\label{PlrcG}
\begin{center}
$\renewcommand{\arraystretch}{1.4}
\begin{array}{|l|c|} \hline
b_{6}=\{e\} & 0 \\
b_{5}=\{s_{3}\} & c\\
b_{4}=\{s_{2},s_{1},s_{1}s_{2},s_{2}s_{1},s_{1}s_{2}s_{1},s_{3}s_{2},s_{2}s_{3},s_{3}s_{2}s_{3},s_{2}s_{1}s_{2}\} & a\\
b_{3}=\{s_{1}s_{3}\}&  a+c\\
b_{2}=\{s_{2}s_{3}s_{2}\} & 2a-c \\
b_{1}= \{w_{2,3}\} & 2a+2c\\
b_{0}= \{w_{1,2}\} & 4a\\ \hline
\end{array}$
\end{center}
\end{table}
}

{\small
\begin{table}[h] \caption{Partition $\mathcal{P}_{\mathfrak{C}}$}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|ccccccc|} \hline
r_{1}=1, r_{2}<1 & b_{0} & b_{1} & \multicolumn{2}{r}{b_{2} \leftrightarrow b_{3}}  & b_{4} & b_{5} & b_{6}\\ \hline
 \end{array}$
\end{center}
\end{table}}

\begin{textblock}{10}(5.775,20)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(-1,0)(-1,-1)
\pspolygon[fillstyle=solid,fillcolor=orange](1,1)(2,2)(1,2)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(0,1)(-1,1)(-.5,.5)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(.5,1.5)(1,2)(1,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(0,-1)(.5,-.5)(1,-1)(1,0)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(.5,.5)(1,0)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0.5,.5)(0,1)(1,1)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$r_{1}=1, r_{2}<1$}

\end{pspicture}
\end{center}

\end{textblock}

\newpage

\item Case $ r_{1}<1, r_{2}<1$

{\small
\begin{table}[h] \caption{Partition $\mathcal{P}_{LR,\mathfrak{C}}$ and values of the $\mathbf{a}$-function}
\label{PlrcG}
\begin{center}
$\renewcommand{\arraystretch}{1.4}
\begin{array}{|l|c|} \hline
b_{8}=\{e\} & 0 \\
b_{7}=\{s_{3}\} & c\\
b_{6}=\{s_{1}\}& a\\
b_{5}=\{s_{1}s_{3}\}&  a+c\\
b_{4}=\{s_{2},s_{1}s_{2},s_{2}s_{1},s_{1}s_{2}s_{1},s_{3}s_{2},s_{2}s_{3},s_{3}s_{2}s_{3}\} & b\\
b_{3}=\{s_{2}s_{1}s_{2}\}& 2b-a\\
b_{2}=\{s_{2}s_{3}s_{2}\} & 2b-c \\
b_{1}= \{w_{2,3}\} & 2b+2c\\
b_{0}= \{w_{1,2}\} & 2a+2b\\ \hline
\end{array}$
\end{center}
\end{table}
}

\vspace{-.3cm}
{\small
\begin{table}[h] \caption{Partition $\mathcal{P}_{\mathfrak{C}}$}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|ccccccccc|} \hline
(r_{1},r_{2})\in B_{2} & b_{0} & b_{1} & b_{2} & b_{3}  & b_{4} & b_{5} & b_{6} & b_{7} & b_{8}\\ \hline

r_{1}+r_{2}-1=0&b_{0} & b_{1} & b_{2} & b_{3} &  \multicolumn{2}{c}{b_{4} \cup b_{5}} & b_{6} & b_{7} & b_{8}\\ \hline

(r_{1},r_{2})\in B_{1}& b_{0} & b_{1} & b_{2} &\multicolumn{2}{l}{b_{3}  \leftrightarrow b_{5}} & b_{4} & b_{6} & b_{7} & b_{8}\\ \hline \end{array}$
\end{center}
\end{table}}

\psset{linewidth=.13mm}

\begin{textblock}{10}(2,14.2)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=Cerulean](0,0)(-1,0)(-1,-1)
\pspolygon[fillstyle=solid,fillcolor=Cerulean](1,1)(2,2)(1,2)

\pspolygon[fillstyle=solid,fillcolor=Plum](0.5,.5)(1,1)(1,0)

\pspolygon[fillstyle=solid,fillcolor=OrangeRed](0,0)(.5,.5)(1,0)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0.5,.5)(0,1)(1,1)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-6)(1,-6)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(-6,0)(-6,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,1)(0,6)(1,6)(1,1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(6,1)(6,0)(1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$(r_{1},r_{2}) \in B_{2}$}

\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(9.55,14,2)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=Cerulean](0,0)(-1,0)(-1,-1)
\pspolygon[fillstyle=solid,fillcolor=Cerulean](1,1)(2,2)(1,2)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,1)(-1,1)(-.5,.5)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,1)(0,2)(.5,1.5)(1,2)(1,1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-1)(.5,-.5)(1,-1)(1,0)

\pspolygon[fillstyle=solid,fillcolor=OrangeRed](0,0)(.5,.5)(1,0)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0.5,.5)(0,1)(1,1)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$r_{1}+r_{2}-1=0$}

\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(5.5,21.1)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=Cerulean](0,0)(-1,0)(-1,-1)
\pspolygon[fillstyle=solid,fillcolor=Cerulean](1,1)(2,2)(1,2)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(0,1)(-1,1)(-.5,.5)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(.5,1.5)(1,2)(1,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(0,-1)(.5,-.5)(1,-1)(1,0)

\pspolygon[fillstyle=solid,fillcolor=OrangeRed](0,0)(.5,.5)(1,0)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0.5,.5)(0,1)(1,1)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$(r_{1},r_{2}) \in B_{1}$}

\end{pspicture}
\end{center}

\end{textblock}

\newpage

\item Case $r_{1}=r_{2}, r_{2}<1$\\

\vspace{-.4cm}

{\small
\begin{table}[htpb] \caption{Partition $\mathcal{P}_{LR,\mathfrak{C}}$ and values of the $\mathbf{a}$-function}
\label{PlrcG}
\begin{center}
$\renewcommand{\arraystretch}{1.3}
\begin{array}{|l|c|} \hline
b_{8}=\{e\} & 0 \\
b_{7}=\{s_{3}\} & a\\
b_{6}=\{s_{1}\}&  a\\
b_{5}=\{s_{1}s_{3}\}&  2a\\
b_{4}=\{s_{2},s_{1}s_{2},s_{2}s_{1},s_{1}s_{2}s_{1},s_{3}s_{2},s_{2}s_{3},s_{3}s_{2}s_{3}\} & b \\
b_{3}=\{s_{2}s_{3}s_{2}\}& 2b-a\\
b_{2}=\{s_{2}s_{1}s_{2}\}& 2b-a\\
b_{1}= \{w_{2,3}\} & 2a+2b\\
b_{0}= \{w_{1,2}\} & 2a+2b\\ \hline
\end{array}$
\end{center}
\end{table}
}

\vspace{-.5cm}

{\small
\begin{table}[htbp] \caption{Partition $\mathcal{P}_{\mathfrak{C}}$}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.3}
$\begin{array}{|c|ccccccc|} \hline
1>r_{2}>1/2 & (b_{0}\cup b_{1}) & (b_{2}\cup b_{3}) & b_{4} & b_{5}  & b_{6} & b_{7} & b_{8}\\ \hline

r_{2}=1/2&(b_{0}\cup b_{1}) & (b_{2}\cup b_{3}) & \multicolumn{2}{r}{b_{4}\cup b_{5} }& b_{6} & b_{7} & b_{8}\\ \hline

r_{2}<1/2&(b_{0}\cup b_{1}) & \multicolumn{2}{r}{(b_{2}\cup b_{3}) \overset{\frac{3}{2}}{\leftrightarrow} b_{5}} & b_{4}  & b_{6} & b_{7} & b_{8}\\ \hline
 \end{array}$
\end{center}
\end{table}}

\psset{linewidth=.13mm}

\begin{textblock}{10}(2,13.5)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-1,0)(-1,-1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(2,2)(1,2)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(0,1)(-1,1)(-.5,.5)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(.5,1.5)(1,2)(1,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(0,-1)(.5,-.5)(1,-1)(1,0)

\pspolygon[fillstyle=solid,fillcolor=OrangeRed](0,0)(.5,.5)(1,0)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0.5,.5)(0,1)(1,1)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$1>r_{2}>1/2$}

\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(9.55,13,5)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-1,0)(-1,-1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(2,2)(1,2)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,.5)(1,1)(1,0)

\pspolygon[fillstyle=solid,fillcolor=OrangeRed](0,0)(.5,.5)(1,0)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0.5,.5)(0,1)(1,1)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-6)(1,-6)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(-6,0)(-6,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,1)(0,6)(1,6)(1,1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(6,1)(6,0)(1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$(r_{1},r_{2})=(1/2,1/2)$}

\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(5.5,20.5)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-1,0)(-1,-1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(2,2)(1,2)

\pspolygon[fillstyle=solid,fillcolor=Plum](0.5,.5)(1,1)(1,0)

\pspolygon[fillstyle=solid,fillcolor=OrangeRed](0,0)(.5,.5)(1,0)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0.5,.5)(0,1)(1,1)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(0,-6)(1,-6)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(-6,0)(-6,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,1)(0,6)(1,6)(1,1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(6,1)(6,0)(1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$ 1/2>r_{2}>0$}

\end{pspicture}
\end{center}

\end{textblock}

$\ $\\
\newpage

\item Case $ r_{1}=r_{2}=1$\\

{\small
\begin{table}[htbp] \caption{Partition $\mathcal{P}_{LR,\mathfrak{C}}$ and values of the $\mathbf{a}$-function}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|l|c|} \hline
b_{4}=\{e\} & 0\\
b_{3}=\mathfrak{C}-b_{0}\cup b_{1}\cup \{e\} & a\\
b_{2}=\{s_{1}s_{3}\}& 2a\\
b_{1}=\{w_{2,3}\}&  4a\\
b_{0}=\{w_{1,2}\}&  4a\\ \hline
 \end{array}$
\end{center}
\end{table}}

{\small
\begin{table}[h] \caption{Partition $\mathcal{P}_{\mathfrak{C}}$}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|cccc|} \hline
r_{2}=r_{1}=1 & b_{0}\cup b_{1} & b_{2} & b_{3} & b_{4}\\ \hline
 \end{array}$
\end{center}
\end{table}}

\psset{linewidth=.13mm}

\begin{textblock}{10}(5.775,11)

\begin{center}
\begin{pspicture}(-6,6)(6,-6)
\psset{linewidth=.13mm}

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,6)(5,6)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-6,6)(-5,6)(-.5,1.5)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0.5,0.5)(1,1)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-0.5,0.5)(-1,1)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0.5,1.5)(5,6)(4,6)(0,2)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-0.5,1.5)(-5,6)(-4,6)(-0,2)

\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(0,2)(1,1)

\pspolygon[fillstyle=solid,fillcolor=purple](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=OrangeRed](0,1)(-.5,1.5)(-1,1)

\pspolygon[fillstyle=solid,fillcolor=red](0,1)(0,2)(-.5,1.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,-1)(0,-6)(1,-6)(1,-1)(.5,-.5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(6,1)(6,0)(2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,1)(-6,1)(-6,0)(-2,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,2)(0,6)(1,6)(1,3)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(0,-1)(.5,-.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(0,2)(1,1)(.5,.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-1,1)(-.5,1.5)(0,1)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,0)(2,0)(6,-4)(6,-5)(0,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,1)(0,2)(-4,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,0)(-2,0)(-6,-4)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,2)(1,3)(1,2)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-.5,.5)(-1,1)(-2,0)(-1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$r_{1}=1$ and $r_{2}=1$}

\end{pspicture}
\end{center}
\end{textblock}

\end{longlist}

$\ $\\

\newpage
\subsection{asymptotic cases}
We now consider the case where some parameters are equal to zero.\\

\begin{longlist}
\item Case $b=0, a,c>0$.  We have
$$W=(\mathbb{Z}/2\mathbb{Z})\ltimes \big(\tilde{A}_{1}\times \tilde{A}_{1}\big)$$
where $\mathbb{Z}/2\mathbb{Z}$ is generated by $I=\{s_{2}\}$ and $\tilde{A}_{1}\times \tilde{A}_{1}$ is generated by $s_{1},s_{2}s_{3}s_{2},s_{3},s_{2}s_{1}s_{2}$. We know that the left (respectively two-sided) cells of $W$ are of the form $W_{I}.C$ (respectively $W_{I}.C.W_{I}$) where $C$ is a left (respectively two-sided) cell of $\tilde{A}_{1}\times \tilde{A}_{1}$ with respect to the weight function $\tilde{L}$ defined by
$$\tilde{L}(s_{1})= \tilde{L}(s_{2}s_{1}s_{2})=a\text{ and } \tilde{L}(s_{3})=\tilde{L}(s_{2}s_{3}s_{2})=c.$$
We obtain the following partition of $W$.

\psset{linewidth=.13mm}
\psset{unit=.5cm}

\begin{textblock}{10}(2,9)
\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0.5,0.5)(1,1)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,0.5)(-1,1)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0.5,1.5)(5,6)(4,6)(0,2)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(-0,2)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,6)(5,6)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-6,6)(-5,6)(-.5,1.5)%

\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(-.5,1.5)(-1,1)(-.5,.5)
\pspolygon[fillstyle=solid,fillcolor=orange](0,1)(.5,1.5)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(-.5,.5)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(-.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,1)(6,0)(2,0)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,0)(-2,0)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(1,6)(1,3)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$b=0, a>c$}

\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(9.55,9)
\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(6,-5)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-.5,.5)(-6,-5)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,6)(5,6)(.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-1,1)(-6,6)(-5,6)(-.5,1.5)%

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(-.5,1.5)(-1,1)(-.5,.5)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(.5,1.5)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(-.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,1)(.5,1.5)(0,2)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-1)(0.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$b=0, a=c$}

\end{pspicture}
\end{center}

\end{textblock}

\vspace{7cm}

\item {\bf Case $c=0$}. \hspace{1cm} We have
$$W=(\mathbb{Z}/2\mathbb{Z})\ltimes \tilde{B}_{2}$$
where $(\mathbb{Z}/2\mathbb{Z})$ is generated by $s_{3}$ and $\tilde{B}_{2}$ is generated by $s_{2},s_{1},s_{3}s_{2}s_{3}$. We know that the left (respectively two-sided) cells of $W$ are of the form $W_{I}.C$ (respectively $W_{I}.C.W_{I}$) where $C$ is a left (respectively two-sided) cell of $\tilde{B}_{2}$ with respect to the weight function $\tilde{L}$ defined by
$$\tilde{L}(s_{1})=a\text{ and } \tilde{L}(s_{2})=\tilde{L}(s_{3}s_{2}s_{3})=b.$$
We obtain the following partition of $W$.

\psset{linewidth=.13mm}

\begin{textblock}{10}(2,21)
\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](1,1)(.5,1.5)(1,2)(2,2)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0,0)(.5,.5)(1,0)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0,0)(-.5,.5)(-1,0)(-1,-1)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=lightgray](0,1)(0,2)(1,1)
\pspolygon[fillstyle=solid,fillcolor=lightgray](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-1)(.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,1)(-1,1)(-.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=lightgray](0,1)(0,2)(-.5,1.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=green!80!black!70!](.5,1.5)(0,2)(1,3)(1,2)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$c=0, b=0, a>0$}
\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(9.55,21)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(0,2)(1,1)
\pspolygon[fillstyle=solid,fillcolor=lightgray](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(0,-1)(.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=Plum](0,1)(-1,1)(-.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=Plum](0,1)(0,2)(-.5,1.5)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(.5,1.5)(1,2)(2,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(.5,.5)(1,0)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(-.5,.5)(-1,0)(-1,-1)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,1.5)(0,2)(1,3)(1,2)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$c=0,a>2b$}
\end{pspicture}
\end{center}

\end{textblock}

\newpage

\begin{textblock}{10}(2,3)
\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(0,2)(1,1)
\pspolygon[fillstyle=solid,fillcolor=lightgray](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(0,-1)(.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,1)(-1,1)(-.5,1.5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,1)(0,2)(-.5,1.5)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,1)(.5,1.5)(1,2)(2,2)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(.5,.5)(1,0)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,0)(-.5,.5)(-1,0)(-1,-1)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](.5,1.5)(0,2)(1,3)(1,2)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$c=0,a=2b$}
\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(9.55,3)
\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=orange](1,1)(.5,1.5)(1,2)(2,2)
\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(.5,.5)(1,0)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=orange](0,0)(-.5,.5)(-1,0)(-1,-1)

\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,0)(-1,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=RedOrange](0,1)(0,2)(1,1)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,1)(1,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(0,-1)(.5,-.5)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0.5,1.5)(0,2)(0,6)(1,6)(1,2)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](.5,.5)(1,1)(6,1)(6,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](.5,-.5)(0,-1)(0,-6)(1,-6)(1,-1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](-.5,.5)(-1,1)(-6,1)(-6,0)(-1,0)

\pspolygon[fillstyle=solid,fillcolor=orange](0.5,0.5)(1,1)(2,0)(1,0)
\pspolygon[fillstyle=solid,fillcolor=orange](-0.5,0.5)(-1,1)(-2,0)(-1,0)
\pspolygon[fillstyle=solid,fillcolor=orange](.5,1.5)(0,2)(1,3)(1,2)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)
\rput(0,-6.7){$c=0,b<a<2b$}
\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(2,10)

\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)
\pspolygon[fillstyle=solid,fillcolor=lightgray](0.5,.5)(0,1)(1,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0.5,.5)(1,1)(1,0)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(.5,.5)(1,0)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-1,0)(-1,-1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(2,2)(1,2)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(0,-6)(1,-6)(1,0)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-6,0)(-6,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(0,6)(1,6)(1,1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,1)(6,0)(1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$c=0,a=b$}

\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(9.55,10)
\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)
\pspolygon[fillstyle=solid,fillcolor=lightgray](0.5,.5)(0,1)(1,1)

\pspolygon[fillstyle=solid,fillcolor=BurntOrange](0.5,.5)(1,1)(1,0)
\pspolygon[fillstyle=solid,fillcolor=BurntOrange](0,0)(.5,.5)(1,0)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=NavyBlue](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=NavyBlue](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=Aquamarine](0,0)(-1,0)(-1,-1)
\pspolygon[fillstyle=solid,fillcolor=RedOrange](1,1)(2,2)(1,2)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(0,-6)(1,-6)(1,0)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-6,0)(-6,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(0,6)(1,6)(1,1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,1)(6,0)(1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$c=0,a<b$}

\end{pspicture}
\end{center}

\end{textblock}

\begin{textblock}{10}(5.55,17)
\begin{center}
\begin{pspicture}(-6,-6)(6,6)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(0,1)(.5,.5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(0,-6)(-6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,-1)(1,-6)(6,-6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](2,0)(6,0)(6,-4)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(6,6)(6,1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,3)(1,6)(4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,2)(0,6)(-4,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,1)(-6,1)(-6,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-2,0)(-6,0)(-6,-4)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,0)(-2,0)(-6,-4)(-6,-5)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,0)(2,0)(6,-4)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,2)(1,3)(4,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-0.5,1.5)(-5,6)(-4,6)(0,2)(0,1)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,1)(-1,1)(-6,6)(-5,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,2)(2,2)(6,6)(5,6)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,0)(1,-1)(6,-6)(6,-5)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](-1,0)(-1,-1)(-6,-6)(-6,-5)

\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](0,0)(-1,0)(-1,-1)
\pspolygon[fillstyle=solid,fillcolor=red!5!yellow!42!](1,1)(2,2)(1,2)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0.5,.5)(1,1)(1,0)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0,0)(.5,.5)(1,0)

\pspolygon[fillstyle=solid,fillcolor=lightgray](0.5,.5)(0,1)(1,1)

\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(0,-6)(1,-6)(1,0)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,0)(-6,0)(-6,1)(0,1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](0,1)(0,6)(1,6)(1,1)
\pspolygon[fillstyle=solid,fillcolor=PineGreen](1,1)(6,1)(6,0)(1,0)

\psline(-6,-6)(-6,6)
\psline(-5,-6)(-5,6)
\psline(-4,-6)(-4,6)
\psline(-3,-6)(-3,6)
\psline(-2,-6)(-2,6)
\psline(-1,-6)(-1,6)
\psline(0,-6)(0,6)
\psline(1,-6)(1,6)
\psline(2,-6)(2,6)
\psline(3,-6)(3,6)
\psline(4,-6)(4,6)
\psline(5,-6)(5,6)
\psline(6,-6)(6,6)

\psline(-6,-6)(6,-6)
\psline(-6,-5)(6,-5)
\psline(-6,-4)(6,-4)
\psline(-6,-3)(6,-3)
\psline(-6,-2)(6,-2)
\psline(-6,-1)(6,-1)
\psline(-6,0)(6,0)
\psline(-6,1)(6,1)
\psline(-6,2)(6,2)
\psline(-6,3)(6,3)
\psline(-6,4)(6,4)
\psline(-6,5)(6,5)
\psline(-6,6)(6,6)

\psline(0,0)(1,1)
\psline(0,1)(1,0)

\psline(1,0)(2,1)
\psline(1,1)(2,0)

\psline(2,0)(3,1)
\psline(2,1)(3,0)

\psline(3,0)(4,1)
\psline(3,1)(4,0)

\psline(4,0)(5,1)
\psline(4,1)(5,0)

\psline(5,0)(6,1)
\psline(5,1)(6,0)

\psline(-1,0)(0,1)
\psline(-1,1)(0,0)

\psline(-2,0)(-1,1)
\psline(-2,1)(-1,0)

\psline(-3,0)(-2,1)
\psline(-3,1)(-2,0)

\psline(-4,0)(-3,1)
\psline(-4,1)(-3,0)

\psline(-5,0)(-4,1)
\psline(-5,1)(-4,0)

\psline(-6,0)(-5,1)
\psline(-6,1)(-5,0)

\psline(0,1)(1,2)
\psline(0,2)(1,1)

\psline(1,1)(2,2)
\psline(1,2)(2,1)

\psline(2,1)(3,2)
\psline(2,2)(3,1)

\psline(3,1)(4,2)
\psline(3,2)(4,1)

\psline(4,1)(5,2)
\psline(4,2)(5,1)

\psline(5,1)(6,2)
\psline(5,2)(6,1)

\psline(-1,1)(0,2)
\psline(-1,2)(0,1)

\psline(-2,1)(-1,2)
\psline(-2,2)(-1,1)

\psline(-3,1)(-2,2)
\psline(-3,2)(-2,1)

\psline(-4,1)(-3,2)
\psline(-4,2)(-3,1)

\psline(-5,1)(-4,2)
\psline(-5,2)(-4,1)

\psline(-6,1)(-5,2)
\psline(-6,2)(-5,1)

\psline(0,2)(1,3)
\psline(0,3)(1,2)

\psline(1,2)(2,3)
\psline(1,3)(2,2)

\psline(2,2)(3,3)
\psline(2,3)(3,2)

\psline(3,2)(4,3)
\psline(3,3)(4,2)

\psline(4,2)(5,3)
\psline(4,3)(5,2)

\psline(5,2)(6,3)
\psline(5,3)(6,2)

\psline(-1,2)(0,3)
\psline(-1,3)(0,2)

\psline(-2,2)(-1,3)
\psline(-2,3)(-1,2)

\psline(-3,2)(-2,3)
\psline(-3,3)(-2,2)

\psline(-4,2)(-3,3)
\psline(-4,3)(-3,2)

\psline(-5,2)(-4,3)
\psline(-5,3)(-4,2)

\psline(-6,2)(-5,3)
\psline(-6,3)(-5,2)

\psline(0,3)( 1,4)
\psline(0,4)( 1,3)

\psline(1,3)( 2,4)
\psline(1,4)( 2,3)

\psline(2,3)( 3,4)
\psline(2,4)( 3,3)

\psline(3,3)( 4,4)
\psline(3,4)( 4,3)

\psline(4,3)( 5,4)
\psline(4,4)( 5,3)

\psline(5,3)( 6,4)
\psline(5,4)( 6,3)

\psline(-1,3)( 0,4)
\psline(-1,4)( 0,3)

\psline(-2,3)( -1,4)
\psline(-2,4)( -1,3)

\psline(-3,3)( -2,4)
\psline(-3,4)( -2,3)

\psline(-4,3)( -3,4)
\psline(-4,4)( -3,3)

\psline(-5,3)( -4,4)
\psline(-5,4)( -4,3)

\psline(-6,3)( -5,4)
\psline(-6,4)( -5,3)

\psline(0,4)(1,5)
\psline(0,5)(1,4)

\psline(1,4)(2,5)
\psline(1,5)(2,4)

\psline(2,4)(3,5)
\psline(2,5)(3,4)

\psline(3,4)(4,5)
\psline(3,5)(4,4)

\psline(4,4)(5,5)
\psline(4,5)(5,4)

\psline(5,4)(6,5)
\psline(5,5)(6,4)

\psline(-1,4)(0,5)
\psline(-1,5)(0,4)

\psline(-2,4)(-1,5)
\psline(-2,5)(-1,4)

\psline(-3,4)(-2,5)
\psline(-3,5)(-2,4)

\psline(-4,4)(-3,5)
\psline(-4,5)(-3,4)

\psline(-5,4)(-4,5)
\psline(-5,5)(-4,4)

\psline(-6,4)(-5,5)
\psline(-6,5)(-5,4)

\psline(0,5)(1,6)
\psline(0,6)(1,5)

\psline(1,5)(2,6)
\psline(1,6)(2,5)

\psline(2,5)(3,6)
\psline(2,6)(3,5)

\psline(3,5)(4,6)
\psline(3,6)(4,5)

\psline(4,5)(5,6)
\psline(4,6)(5,5)

\psline(5,5)(6,6)
\psline(5,6)(6,5)

\psline(-1,5)(0,6)
\psline(-1,6)(0,5)

\psline(-2,5)(-1,6)
\psline(-2,6)(-1,5)

\psline(-3,5)(-2,6)
\psline(-3,6)(-2,5)

\psline(-4,5)(-3,6)
\psline(-4,6)(-3,5)

\psline(-5,5)(-4,6)
\psline(-5,6)(-4,5)

\psline(-6,5)(-5,6)
\psline(-6,6)(-5,5)

\psline(0,0)(1,-1)
\psline(0,-1)(1,0)

\psline(1,0)(2,-1)
\psline(1,-1)(2,0)

\psline(2,0)(3,-1)
\psline(2,-1)(3,0)

\psline(3,0)(4,-1)
\psline(3,-1)(4,0)

\psline(4,0)(5,-1)
\psline(4,-1)(5,0)

\psline(5,0)(6,-1)
\psline(5,-1)(6,0)

\psline(-1,0)(0,-1)
\psline(-1,-1)(0,0)

\psline(-2,0)(-1,-1)
\psline(-2,-1)(-1,0)

\psline(-3,0)(-2,-1)
\psline(-3,-1)(-2,0)

\psline(-4,0)(-3,-1)
\psline(-4,-1)(-3,0)

\psline(-5,0)(-4,-1)
\psline(-5,-1)(-4,0)

\psline(-6,0)(-5,-1)
\psline(-6,-1)(-5,0)

\psline(0,-1)(1,-2)
\psline(0,-2)(1,-1)

\psline(1,-1)(2,-2)
\psline(1,-2)(2,-1)

\psline(2,-1)(3,-2)
\psline(2,-2)(3,-1)

\psline(3,-1)(4,-2)
\psline(3,-2)(4,-1)

\psline(4,-1)(5,-2)
\psline(4,-2)(5,-1)

\psline(5,-1)(6,-2)
\psline(5,-2)(6,-1)

\psline(-1,-1)(0,-2)
\psline(-1,-2)(0,-1)

\psline(-2,-1)(-1,-2)
\psline(-2,-2)(-1,-1)

\psline(-3,-1)(-2,-2)
\psline(-3,-2)(-2,-1)

\psline(-4,-1)(-3,-2)
\psline(-4,-2)(-3,-1)

\psline(-5,-1)(-4,-2)
\psline(-5,-2)(-4,-1)

\psline(-6,-1)(-5,-2)
\psline(-6,-2)(-5,-1)

\psline(0,-2)(1,-3)
\psline(0,-3)(1,-2)

\psline(1,-2)(2,-3)
\psline(1,-3)(2,-2)

\psline(2,-2)(3,-3)
\psline(2,-3)(3,-2)

\psline(3,-2)(4,-3)
\psline(3,-3)(4,-2)

\psline(4,-2)(5,-3)
\psline(4,-3)(5,-2)

\psline(5,-2)(6,-3)
\psline(5,-3)(6,-2)

\psline(-1,-2)(0,-3)
\psline(-1,-3)(0,-2)

\psline(-2,-2)(-1,-3)
\psline(-2,-3)(-1,-2)

\psline(-3,-2)(-2,-3)
\psline(-3,-3)(-2,-2)

\psline(-4,-2)(-3,-3)
\psline(-4,-3)(-3,-2)

\psline(-5,-2)(-4,-3)
\psline(-5,-3)(-4,-2)

\psline(-6,-2)(-5,-3)
\psline(-6,-3)(-5,-2)

\psline(0,-3)( 1,-4)
\psline(0,-4)( 1,-3)

\psline(1,-3)( 2,-4)
\psline(1,-4)( 2,-3)

\psline(2,-3)( 3,-4)
\psline(2,-4)( 3,-3)

\psline(3,-3)( 4,-4)
\psline(3,-4)( 4,-3)

\psline(4,-3)( 5,-4)
\psline(4,-4)( 5,-3)

\psline(5,-3)( 6,-4)
\psline(5,-4)( 6,-3)

\psline(-1,-3)( 0,-4)
\psline(-1,-4)( 0,-3)

\psline(-2,-3)( -1,-4)
\psline(-2,-4)( -1,-3)

\psline(-3,-3)( -2,-4)
\psline(-3,-4)( -2,-3)

\psline(-4,-3)( -3,-4)
\psline(-4,-4)( -3,-3)

\psline(-5,-3)( -4,-4)
\psline(-5,-4)( -4,-3)

\psline(-6,-3)( -5,-4)
\psline(-6,-4)( -5,-3)

\psline(0,-4)(1,-5)
\psline(0,-5)(1,-4)

\psline(1,-4)(2,-5)
\psline(1,-5)(2,-4)

\psline(2,-4)(3,-5)
\psline(2,-5)(3,-4)

\psline(3,-4)(4,-5)
\psline(3,-5)(4,-4)

\psline(4,-4)(5,-5)
\psline(4,-5)(5,-4)

\psline(5,-4)(6,-5)
\psline(5,-5)(6,-4)

\psline(-1,-4)(0,-5)
\psline(-1,-5)(0,-4)

\psline(-2,-4)(-1,-5)
\psline(-2,-5)(-1,-4)

\psline(-3,-4)(-2,-5)
\psline(-3,-5)(-2,-4)

\psline(-4,-4)(-3,-5)
\psline(-4,-5)(-3,-4)

\psline(-5,-4)(-4,-5)
\psline(-5,-5)(-4,-4)

\psline(-6,-4)(-5,-5)
\psline(-6,-5)(-5,-4)

\psline(0,-5)(1,-6)
\psline(0,-6)(1,-5)

\psline(1,-5)(2,-6)
\psline(1,-6)(2,-5)

\psline(2,-5)(3,-6)
\psline(2,-6)(3,-5)

\psline(3,-5)(4,-6)
\psline(3,-6)(4,-5)

\psline(4,-5)(5,-6)
\psline(4,-6)(5,-5)

\psline(5,-5)(6,-6)
\psline(5,-6)(6,-5)

\psline(-1,-5)(0,-6)
\psline(-1,-6)(0,-5)

\psline(-2,-5)(-1,-6)
\psline(-2,-6)(-1,-5)

\psline(-3,-5)(-2,-6)
\psline(-3,-6)(-2,-5)

\psline(-4,-5)(-3,-6)
\psline(-4,-6)(-3,-5)

\psline(-5,-5)(-4,-6)
\psline(-5,-6)(-4,-5)

\psline(-6,-5)(-5,-6)
\psline(-6,-6)(-5,-5)

\rput(0,-6.7){$c=0,a=0,b>0$}

\end{pspicture}
\end{center}

\end{textblock}

\end{longlist}

$\ $\\

\newpage

\section{Proof of \cite[Theorem 5.3]{jeju4} for $\tilde{B}_{2}$ }
\label{sec4}

As for $\tilde{G}_{2}$ (see Section 3), in each case we give the partial order $\preceq$ on $U$ (which is also the left order on the left cells) and a table for Condition {\bf I5}. When we have $T_{x}C_{u}\equiv T_{xu}$ we do not put it in the table. So when there is no table it means that $T_{x}C_{u}\equiv T_{xu}\mod \mathcal{H}_{<0}$ for all $u\in U$ and $x\in X_{u}$.

\begin{longlist}

\item {\bf Case $(r_{1},r_{2})\in C_{3}$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](-.5,1.5)(0,2)
\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,1.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,1)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](0,2)(1,3)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](1,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,1)(-2,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(1.2,.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{3}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{3}}$}}

\rput(-.2,1.5){{\small $ {\bf \tilde{c}^1_{4}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(-.5,1.2){{\small $ {\bf \tilde{c}^2_{6}}$}}
\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{6}}$}}

\rput(-.2,.5){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{textblock}{21}(0,14.5)
\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](1,2){.35}
\rput(1,2){{\footnotesize $u^1_{1}$}}

\pscircle(5,2){.35}
\rput(5,2){{\footnotesize $u^2_{1}$}}

\pscircle(9,2){.35}
\rput(9,2){{\footnotesize $u^3_{1}$}}

\pscircle(13,2){.35}
\rput(13,2){{\footnotesize $u^4_{1}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](5,4){.35}
\rput(5,4){{\footnotesize $u^1_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^2_{2}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](10.5,4){.35}
\rput(10.5,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(5,6){.35}
\rput(5,6){{\footnotesize $u^1_{3}$}}

\pscircle(8.5,6){.35}
\rput(8.5,6){{\footnotesize $u^2_{3}$}}

\pscircle(10.5,6){.35}
\rput(10.5,6){{\footnotesize $u^3_{3}$}}

\pscircle(13,6){.35}
\rput(13,6){{\footnotesize $u^4_{3}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](9.5,7){.35}
\rput(9.5,7){{\footnotesize $u^{1}_{4}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](9,9){.35}
\rput(9,9){{\footnotesize $u^{1}_{5}$}}

\pscircle(8.5,11){.35}
\rput(8.5,11){{\footnotesize $u^1_{6}$}}

\pscircle(11.5,11){.35}
\rput(11.5,11){{\footnotesize $u^2_{6}$}}

\pscircle(12.5,12.5){.35}
\rput(12.5,12.5){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(10,13.65)(12.5,12.85)
\psline(10,13.65)(8.5,11.35)
\psline(10,13.65)(6.5,12.5)(5,6.35)

\psline(10.5,3.65)(10,.35)

\psline(9.5,6.65)(10.5,4.35)

\psline(1,1.65)(0,.35)
\psline(1,1.65)(2,.35)

\psline(5,1.65)(4,.35)
\psline(5,1.65)(6,.35)

\psline(9,1.65)(10,.35)
\psline(9,1.65)(8,.35)

\psline(13,1.65)(14,.35)
\psline(13,1.65)(12,.35)

\psline(5,3.65)(5,2.35)

\psline(9,3.65)(9,2.35)

\psline(13,3.65)(13,2.35)

\psline(5,5.65)(1,2.35)
\psline(5,5.65)(5,4.35)

\psline(8.5,5.65)(9,4.35)
\psline(8.5,5.65)(5,4.35)

\psline(13,5.65)(13,4.35)
\psline(13,5.65)(16,.35)

\psline(10.5,5.65)(13,4.35)
\psline(10.5,5.65)(10.5,4.35)

\psline(9,8.65)(9.5,7.35)
\psline(9,8.65)(9,4.35)

\psline(8.5,10.65)(9,9.35)
\psline(8.5,10.65)(8.5,6.35)
\psline(8.5,10.65)(5,4.35)

\psline(11.5,10.65)(9.5,7.35)
\psline(11.5,10.65)(10.5,6.35)

\psline(12.5,12.15)(11.5,11.35)
\psline(12.5,12.15)(13,6.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}
\end{textblock}

\newpage

\item {\bf Case $r_{1}-r_{2}-2=0$, $r_{2}>1$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,1.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,1)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](0,2)(1,3)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](1,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,1)(-2,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(1.2,.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{3}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{3}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(-.5,1.2){{\small $ {\bf \tilde{c}^2_{6}}$}}
\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{6}}$}}

\rput(-.2,.5){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](1,2){.35}
\rput(1,2){{\footnotesize $u^1_{1}$}}

\pscircle(5,2){.35}
\rput(5,2){{\footnotesize $u^2_{1}$}}

\pscircle(9,2){.35}
\rput(9,2){{\footnotesize $u^3_{1}$}}

\pscircle(13,2){.35}
\rput(13,2){{\footnotesize $u^4_{1}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](5,4){.35}
\rput(5,4){{\footnotesize $u^1_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^2_{2}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](10.5,4){.35}
\rput(10.5,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(5,6){.35}
\rput(5,6){{\footnotesize $u^1_{3}$}}

\pscircle(8.5,6){.35}
\rput(8.5,6){{\footnotesize $u^2_{3}$}}

\pscircle(10.5,6){.35}
\rput(10.5,6){{\footnotesize $u^3_{3}$}}

\pscircle(13,6){.35}
\rput(13,6){{\footnotesize $u^4_{3}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](9,9){.35}
\rput(9,9){{\footnotesize $u^{1}_{5}$}}

\pscircle(8.5,11){.35}
\rput(8.5,11){{\footnotesize $u^1_{6}$}}

\pscircle(11.5,11){.35}
\rput(11.5,11){{\footnotesize $u^2_{6}$}}

\pscircle(12.5,12.5){.35}
\rput(12.5,12.5){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(10,13.65)(12.5,12.85)
\psline(10,13.65)(8.5,11.35)
\psline(10,13.65)(6.5,12.5)(5,6.35)

\psline(10.5,3.65)(10,.35)

\psline(1,1.65)(0,.35)
\psline(1,1.65)(2,.35)

\psline(5,1.65)(4,.35)
\psline(5,1.65)(6,.35)

\psline(9,1.65)(10,.35)
\psline(9,1.65)(8,.35)

\psline(13,1.65)(14,.35)
\psline(13,1.65)(12,.35)

\psline(5,3.65)(5,2.35)

\psline(9,3.65)(9,2.35)

\psline(13,3.65)(13,2.35)

\psline(5,5.65)(1,2.35)
\psline(5,5.65)(5,4.35)

\psline(8.5,5.65)(9,4.35)
\psline(8.5,5.65)(5,4.35)

\psline(13,5.65)(13,4.35)
\psline(13,5.65)(16,.35)

\psline(10.5,5.65)(13,4.35)
\psline(10.5,5.65)(10.5,4.35)

\psline(9,8.65)(10.5,4.35)
\psline(9,8.65)(9,4.35)

\psline(8.5,10.65)(9,9.35)
\psline(8.5,10.65)(8.5,6.35)
\psline(8.5,10.65)(5,4.35)

\psline(11.5,10.65)(10.5,6.35)

\psline(12.5,12.15)(11.5,11.35)
\psline(12.5,12.15)(13,6.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

\item {\bf Case $(r_{1},r_{2})\in C_{2}$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](-1,0)(-2,0)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,1.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,1)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](0,2)(1,3)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](1,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,1)(-2,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(2.2,-.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(.5,1.8){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-1.2,.5){{\small $ {\bf \tilde{c}^3_{3}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{4}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{4}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(-.5,1.2){{\small $ {\bf \tilde{c}^2_{6}}$}}
\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{6}}$}}

\rput(-.2,.5){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](1,2){.35}
\rput(1,2){{\footnotesize $u^1_{1}$}}

\pscircle(6,2){.35}
\rput(6,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{2}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{2}$}}

\pscircle(11,2){.35}
\rput(11,2){{\footnotesize $u^3_{2}$}}

\pscircle(12,2){.35}
\rput(12,2){{\footnotesize $u^4_{2}$}}

\pscircle(5,5){.35}
\rput(5,5){{\footnotesize $u^1_{3}$}}

\pscircle(9,5){.35}
\rput(9,5){{\footnotesize $u^2_{3}$}}

\pscircle(13,5){.35}
\rput(13,5){{\footnotesize $u^3_{3}$}}

\pscircle(3,7){.35}
\rput(3,7){{\footnotesize $u^{1}_{4}$}}

\pscircle(7,7){.35}
\rput(7,7){{\footnotesize $u^{2}_{4}$}}

\pscircle(11,7){.35}
\rput(11,7){{\footnotesize $u^{3}_{4}$}}

\pscircle(15,7){.35}
\rput(15,7){{\footnotesize $u^{4}_{4}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](9,9){.35}
\rput(9,9){{\footnotesize $u^{1}_{5}$}}

\pscircle(7,11){.35}
\rput(7,11){{\footnotesize $u^1_{6}$}}

\pscircle(12,11){.35}
\rput(12,11){{\footnotesize $u^2_{6}$}}

\pscircle(13,12.5){.35}
\rput(13,12.5){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(1,1.65)(0,.35)
\psline(1,1.65)(2,.35)

\psline(6,1.65)(4,.35)
\psline(6,1.65)(6,.35)

\psline(10,1.65)(10,.35)
\psline(10,1.65)(8,.35)

\psline(14,1.65)(14,.35)
\psline(14,1.65)(12,.35)

\psline(4,1.65)(4,.35)
\psline(4,1.65)(6,.35)

\psline(8,1.65)(8,.35)
\psline(8,1.65)(10,.35)

\psline(11,1.65)(10,.35)

\psline(12,1.65)(14,.35)
\psline(12,1.65)(12,.35)

\psline(5,4.65)(6,2.35)
\psline(5,4.65)(4,2.35)

\psline(9,4.65)(10,2.35)
\psline(9,4.65)(8,2.35)

\psline(13,4.65)(12,2.35)
\psline(13,4.65)(14,2.35)

\psline(3,6.65)(1,2.35)
\psline(3,6.65)(5,5.35)

\psline(7,6.65)(9,5.35)
\psline(7,6.65)(5,5.35)

\psline(11,6.65)(11,2.35)
\psline(11,6.65)(13,5.35)

\psline(15,6.65)(13,5.35)
\psline(15,6.65)(16,.35)

\psline(9,8.65)(9,5.35)
\psline(9,8.65)(11,2.35)

\psline(7,10.65)(9,9.35)
\psline(7,10.65)(7,7.35)
\psline(7,10.65)(5,5.35)

\psline(12,10.65)(11,7.35)
\psline(12,10.65)(13,5.35)

\psline(13,12.15)(12,11.35)
\psline(13,12.15)(15,7.35)

\psline(10,13.65)(13,12.85)
\psline(10,13.65)(7,11.35)
\psline(10,13.65)(6.5,12.5)(3,7.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

\item {\bf Case $r_{1}-r_{2}-1=0$, $r_{2}>1$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](-1,0)(-2,0)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,1.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](1,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(2.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(.2,-1.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{4}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{4}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(-.5,1.2){{\small $ {\bf \tilde{c}^2_{6}}$}}
\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{6}}$}}

\rput(-.2,.5){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(1,4){.35}
\rput(1,4){{\footnotesize $u^1_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^2_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(3,7){.35}
\rput(3,7){{\footnotesize $u^{1}_{4}$}}

\pscircle(7,7){.35}
\rput(7,7){{\footnotesize $u^{2}_{4}$}}

\pscircle(11,7){.35}
\rput(11,7){{\footnotesize $u^{3}_{4}$}}

\pscircle(15,7){.35}
\rput(15,7){{\footnotesize $u^{4}_{4}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](9,9){.35}
\rput(9,9){{\footnotesize $u^{1}_{5}$}}

\pscircle(7,11){.35}
\rput(7,11){{\footnotesize $u^1_{6}$}}

\pscircle(12,11){.35}
\rput(12,11){{\footnotesize $u^2_{6}$}}

\pscircle(13,12.5){.35}
\rput(13,12.5){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(4,1.65)(4,.35)
\psline(4,1.65)(6,.35)

\psline(8,1.65)(8,.35)
\psline(8,1.65)(10,.35)

\psline(10,1.65)(10,.35)
\psline(14,1.65)(14,.35)
\psline(14,1.65)(12,.35)

\psline(1,3.65)(0,.35)
\psline(1,3.65)(2,.35)

\psline(5,3.65)(4,2.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)

\psline(13,3.65)(14,2.35)

\psline(3,6.65)(1,4.35)
\psline(3,6.65)(5,4.35)

\psline(7,6.65)(5,4.35)
\psline(7,6.65)(9,4.35)

\psline(11,6.65)(13,4.35)
\psline(11,6.65)(10,2.35)

\psline(15,6.65)(13,4.35)
\psline(15,6.65)(16,.35)

\psline(9,8.65)(9,4.35)

\psline(7,10.65)(9,9.35)
\psline(7,10.65)(7,7.35)

\psline(12,10.65)(11,7.35)

\psline(13,12.15)(12,11.35)
\psline(13,12.15)(15,7.35)

\psline(10,13.65)(7,11.35)
\psline(10,13.65)(13,12.85)
\psline(10,13.65)(5,11)(3,7.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

\item {\bf Case $(r_{1},r_{2})\in C_{1}$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](-1,0)(-2,0)

\psline[linewidth=.7mm](0,-1)(.5,-.5)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,1.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](1,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(2.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(.2,-1.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{4}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{4}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(-.5,1.2){{\small $ {\bf \tilde{c}^2_{6}}$}}
\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{6}}$}}

\rput(-.2,.5){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(1,4){.35}
\rput(1,4){{\footnotesize $u^1_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^2_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(1,5){.35}
\rput(1,5){{\footnotesize $u^1_{3}$}}

\pscircle(3,7){.35}
\rput(3,7){{\footnotesize $u^{1}_{4}$}}

\pscircle(7,7){.35}
\rput(7,7){{\footnotesize $u^{2}_{4}$}}

\pscircle(11,7){.35}
\rput(11,7){{\footnotesize $u^{3}_{4}$}}

\pscircle(15,7){.35}
\rput(15,7){{\footnotesize $u^{4}_{4}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](9,9){.35}
\rput(9,9){{\footnotesize $u^{1}_{5}$}}

\pscircle(7,11){.35}
\rput(7,11){{\footnotesize $u^1_{6}$}}

\pscircle(12,11){.35}
\rput(12,11){{\footnotesize $u^2_{6}$}}

\pscircle(13,12.5){.35}
\rput(13,12.5){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(4,1.65)(4,.35)
\psline(8,1.65)(8,.35)
\psline(10,1.65)(10,.35)
\psline(14,1.65)(14,.35)

\psline(1,3.65)(0,.35)
\psline(1,3.65)(2,.35)

\psline(5,3.65)(4,2.35)
\psline(5,3.65)(6,.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)

\psline(13,3.65)(12,.35)
\psline(13,3.65)(14,2.35)

\psline(1,4.65)(1,4.35)

\psline(3,6.65)(1,5.35)
\psline(3,6.65)(5,4.35)

\psline(7,6.65)(5,4.35)
\psline(7,6.65)(9,4.35)

\psline(11,6.65)(13,4.35)
\psline(11,6.65)(10,2.35)

\psline(15,6.65)(13,4.35)
\psline(15,6.65)(16,.35)

\psline(9,8.65)(9,4.35)

\psline(7,10.65)(9,9.35)
\psline(7,10.65)(7,7.35)

\psline(12,10.65)(11,7.35)

\psline(13,12.15)(12,11.35)
\psline(13,12.15)(15,7.35)

\psline(10,13.65)(7,11.35)
\psline(10,13.65)(13,12.85)
\psline(10,13.65)(5,11)(3,7.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\vspace{.8cm}
Let $w=s_{1}s_{3}s_{2}s_{1}s_{3}s_{2}$ and $w_{1}=s_{1}s_{2}s_{3}s_{2}$. In the following table
$$y\in \{zw^{n}|z\in Y(w), n\in \mathbb{N}\} \text{ and } y_{1}\in \{zw^{n}|z\in Y(w_{1}), n\in \mathbb{N}\} .$$
$\ $\\

{\small
\begin{table}[htbp] \caption{Condition {\bf I5} }
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{2}^{1} & s_{1}s_{2} & T_{xu} +v^{a-c}\hspace{2pt} C_{u_{0}^{1}}\\\hline
u_{2}^{1} & ys_{1}s_{3}s_{2} & T_{xu} +v^{a-c}\hspace{2pt} T_{ys_{3}}C_{u_{0}^{1}}\\\hline
u_{4}^{3} & s_{2}s_{3}s_{2} & T_{xu}+v^{-a+2b}\hspace{2pt} C_{u_{1}^{3}}\\\hline
u_{4}^{3} & y_{1}s_{1}s_{2}s_{3}s_{2} & T_{xu} +v^{-a+2b}\hspace{2pt} T_{y_{1}s_{1}}C_{u_{1}^{3}}\\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item {\bf Case $ r_{1}=r_{2}, r_{2}>1$}

$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](-1,0)(-2,0)

\psline[linewidth=.7mm](0,-1)(.5,-.5)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,1.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)

\psline[linewidth=.7mm](1,3)(1,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)

\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,.5)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(.2,-1.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{6}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{6}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{6}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{6}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(-.2,.5){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.61cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(1,4){.35}
\rput(1,4){{\footnotesize $u^1_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^2_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(1,5){.35}
\rput(1,5){{\footnotesize $u^1_{3}$}}

\pscircle(3,7){.35}
\rput(3,7){{\footnotesize $u^{1}_{6}$}}

\pscircle(7,7){.35}
\rput(7,7){{\footnotesize $u^{2}_{6}$}}

\pscircle(11,7){.35}
\rput(11,7){{\footnotesize $u^{3}_{6}$}}

\pscircle(15,7){.35}
\rput(15,7){{\footnotesize $u^{4}_{6}$}}

\pscircle(9,6){.35}
\rput(9,6){{\footnotesize $u^{1}_{5}$}}

\pscircle(13,12.5){.35}
\rput(13,12.5){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(1,3.65)(0,.35)
\psline(1,3.65)(2,.35)

\psline(5,3.65)(4,.35)
\psline(5,3.65)(6,.35)

\psline(9,3.65)(8,.35)
\psline(9,3.65)(10,.35)

\psline(13,3.65)(12,.35)
\psline(13,3.65)(14,.35)

\psline(1,4.65)(1,4.35)

\psline(3,6.65)(1,5.35)
\psline(3,6.65)(5,4.35)

\psline(7,6.65)(5,4.35)
\psline(7,6.65)(9,6.35)

\psline(11,6.65)(13,4.35)
\psline(11,6.65)(10,.35)

\psline(15,6.65)(13,4.35)
\psline(15,6.65)(16,.35)

\psline(9,5.65)(9,4.35)

\psline(13,12.15)(11,7.35)
\psline(13,12.15)(15,7.35)

\psline(10,13.65)(7,7.35)
\psline(10,13.65)(13,12.85)
\psline(10,13.65)(5,11)(3,7.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\vspace{1cm}

Let $w=s_{1}s_{3}s_{2}s_{1}s_{3}s_{2}$. In the following table
$$y\in \{zw^{n}| y\in Y(w), n\in\mathbb{N}\}.$$

{\small
\begin{table}[h!] \caption{Condition {\bf I5}}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{2}^{1} & s_{1}s_{2} & T_{xu} +\hspace{2pt} C_{u_{0}^{1}}\\\hline
u_{2}^{1} & ys_{1}s_{3}s_{2} & T_{xu} +\hspace{2pt} T_{ys_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{3} & s_{3}s_{2} & T_{xu}+\hspace{2pt} C_{u_{0}^{6}}\\\hline
u_{2}^{3} & ys_{1}s_{3}s_{2} & T_{xu} +\hspace{2pt} T_{ys_{1}}C_{u_{0}^{6}}\\\hline

 \end{array}$
\end{center}
\end{table}}

$\ $\\

\newpage

\item{\bf Case $r_{1}>3,r_{2}=1$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](-.5,1.5)(0,2)
\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,1)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](0,2)(1,3)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](1,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,1)(-2,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(1.2,.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{3}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{3}}$}}

\rput(-.2,1.5){{\small $ {\bf \tilde{c}^1_{4}}$}}

\rput(-.5,1.2){{\small $ {\bf \tilde{c}^2_{6}}$}}
\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{6}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](1,2){.35}
\rput(1,2){{\footnotesize $u^1_{1}$}}

\pscircle(5,2){.35}
\rput(5,2){{\footnotesize $u^2_{1}$}}

\pscircle(9,2){.35}
\rput(9,2){{\footnotesize $u^3_{1}$}}

\pscircle(13,2){.35}
\rput(13,2){{\footnotesize $u^4_{1}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](5,4){.35}
\rput(5,4){{\footnotesize $u^1_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^2_{2}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](10.5,4){.35}
\rput(10.5,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(5,6){.35}
\rput(5,6){{\footnotesize $u^1_{3}$}}

\pscircle(8.5,6){.35}
\rput(8.5,6){{\footnotesize $u^2_{3}$}}

\pscircle(10.5,6){.35}
\rput(10.5,6){{\footnotesize $u^3_{3}$}}

\pscircle(13,6){.35}
\rput(13,6){{\footnotesize $u^4_{3}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](9.5,7){.35}
\rput(9.5,7){{\footnotesize $u^{1}_{4}$}}

\pscircle(8.5,11){.35}
\rput(8.5,11){{\footnotesize $u^1_{6}$}}

\pscircle(11.5,11){.35}
\rput(11.5,11){{\footnotesize $u^2_{6}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(10,13.65)(11.5,11.35)
\psline(10,13.65)(8.5,11.35)
\psline(10,13.65)(6.5,12.5)(5,6.35)

\psline(10.5,3.65)(10,.35)

\psline(9.5,6.65)(10.5,4.35)

\psline(1,1.65)(0,.35)
\psline(1,1.65)(2,.35)

\psline(5,1.65)(4,.35)
\psline(5,1.65)(6,.35)

\psline(9,1.65)(10,.35)
\psline(9,1.65)(8,.35)
\psline(9,1.65)(6,.35)

\psline(13,1.65)(14,.35)
\psline(13,1.65)(12,.35)
\psline(13,1.65)(16,.35)

\psline(5,3.65)(5,2.35)

\psline(9,3.65)(9,2.35)

\psline(13,3.65)(13,2.35)

\psline(5,5.65)(1,2.35)
\psline(5,5.65)(5,4.35)

\psline(8.5,5.65)(9,4.35)
\psline(8.5,5.65)(5,4.35)

\psline(13,5.65)(13,4.35)
\psline(13,5.65)(16,.35)

\psline(10.5,5.65)(13,4.35)
\psline(10.5,5.65)(10.5,4.35)

\psline(8.5,10.65)(9.5,7.35)
\psline(8.5,10.65)(8.5,6.35)
\psline(8.5,10.65)(5,4.35)

\psline(11.5,10.65)(9.5,7.35)
\psline(11.5,10.65)(10.5,6.35)
\psline(11.5,10.65)(13,6.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

\item{\bf Case $r_{1}=3,r_{2}=1$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,1)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](0,2)(1,3)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](1,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,1)(-2,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(1.2,.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{3}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{3}}$}}

\rput(-.5,1.2){{\small $ {\bf \tilde{c}^2_{6}}$}}
\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{6}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](1,2){.35}
\rput(1,2){{\footnotesize $u^1_{1}$}}

\pscircle(5,2){.35}
\rput(5,2){{\footnotesize $u^2_{1}$}}

\pscircle(9,2){.35}
\rput(9,2){{\footnotesize $u^3_{1}$}}

\pscircle(13,2){.35}
\rput(13,2){{\footnotesize $u^4_{1}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](5,4){.35}
\rput(5,4){{\footnotesize $u^1_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^2_{2}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](10.5,4){.35}
\rput(10.5,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(5,6){.35}
\rput(5,6){{\footnotesize $u^1_{3}$}}

\pscircle(8.5,6){.35}
\rput(8.5,6){{\footnotesize $u^2_{3}$}}

\pscircle(10.5,6){.35}
\rput(10.5,6){{\footnotesize $u^3_{3}$}}

\pscircle(13,6){.35}
\rput(13,6){{\footnotesize $u^4_{3}$}}

\pscircle(8.5,11){.35}
\rput(8.5,11){{\footnotesize $u^1_{6}$}}

\pscircle(11.5,11){.35}
\rput(11.5,11){{\footnotesize $u^2_{6}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(10,13.65)(11.5,11.35)
\psline(10,13.65)(8.5,11.35)
\psline(10,13.65)(6.5,12.5)(5,6.35)

\psline(10.5,3.65)(10,.35)

\psline(1,1.65)(0,.35)
\psline(1,1.65)(2,.35)

\psline(5,1.65)(4,.35)
\psline(5,1.65)(6,.35)

\psline(9,1.65)(10,.35)
\psline(9,1.65)(8,.35)
\psline(9,1.65)(6,.35)

\psline(13,1.65)(14,.35)
\psline(13,1.65)(12,.35)
\psline(13,1.65)(16,.35)

\psline(5,3.65)(5,2.35)

\psline(9,3.65)(9,2.35)

\psline(13,3.65)(13,2.35)

\psline(5,5.65)(1,2.35)
\psline(5,5.65)(5,4.35)

\psline(8.5,5.65)(9,4.35)
\psline(8.5,5.65)(5,4.35)

\psline(13,5.65)(13,4.35)

\psline(10.5,5.65)(13,4.35)
\psline(10.5,5.65)(10.5,4.35)

\psline(8.5,10.65)(10.5,4.35)
\psline(8.5,10.65)(8.5,6.35)
\psline(8.5,10.65)(5,4.35)

\psline(11.5,10.65)(10.5,6.35)
\psline(11.5,10.65)(13,6.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

\item{\bf Case $2<r_{1}<3,r_{2}=1$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](-1,0)(-2,0)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,1)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](0,2)(1,3)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](1,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,1)(-2,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(2.2,-.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(.5,2.2){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-1.2,.5){{\small $ {\bf \tilde{c}^3_{3}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(-1.8,2.5){{\small $ {\bf \tilde{c}^3_{4}}$}}
\rput(-1.8,-1.5){{\small $ {\bf \tilde{c}^4_{4}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{6}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^2_{6}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](1,2){.35}
\rput(1,2){{\footnotesize $u^1_{1}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^2_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^3_{1}$}}

\pscircle(13,2){.35}
\rput(13,2){{\footnotesize $u^4_{1}$}}

\pscircle(6,2){.35}
\rput(6,2){{\footnotesize $u^1_{2}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^2_{2}$}}

\pscircle(11,2){.35}
\rput(11,2){{\footnotesize $u^3_{2}$}}

\pscircle(15,2){.35}
\rput(15,2){{\footnotesize $u^4_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^1_{3}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^2_{3}$}}

\pscircle(14,4){.35}
\rput(14,4){{\footnotesize $u^3_{3}$}}

\pscircle(3,6){.35}
\rput(3,6){{\footnotesize $u^{1}_{4}$}}

\pscircle(9,6){.35}
\rput(9,6){{\footnotesize $u^{2}_{4}$}}

\pscircle(12,6){.35}
\rput(12,6){{\footnotesize $u^{3}_{4}$}}

\pscircle(14,6){.35}
\rput(14,6){{\footnotesize $u^{4}_{4}$}}

\pscircle(9,10){.35}
\rput(9,10){{\footnotesize $u^1_{6}$}}

\pscircle(13,10){.35}
\rput(13,10){{\footnotesize $u^2_{6}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(1,1.65)(0,.35)
\psline(1,1.65)(2,.35)

\psline(4,1.65)(4,.35)
\psline(4,1.65)(6,.35)

\psline(8,1.65)(8,.35)
\psline(8,1.65)(10,.35)
\psline(8,1.65)(6,.35)

\psline(13,1.65)(12,.35)
\psline(13,1.65)(14,.35)
\psline(13,1.65)(16,.35)

\psline(6,1.65)(4,.35)
\psline(6,1.65)(6,.35)

\psline(10,1.65)(8,.35)
\psline(10,1.65)(10,.35)
\psline(10,1.65)(6,.35)

\psline(11,1.65)(10,.35)

\psline(15,1.65)(12,.35)
\psline(15,1.65)(14,.35)
\psline(15,1.65)(16,.35)

\psline(5,3.65)(4,2.35)
\psline(5,3.65)(6,2.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)

\psline(14,3.65)(13,2.35)
\psline(14,3.65)(15,2.35)

\psline(3,5.65)(1,2.35)
\psline(3,5.65)(5,4.35)

\psline(9,5.65)(9,4.35)
\psline(9,5.65)(5,4.35)

\psline(12,5.65)(11,2.35)
\psline(12,5.65)(12,.35)
\psline(12,5.65)(14,4.35)

\psline(14,5.65)(14,4.35)

\psline(9,9.65)(9,6.35)
\psline(9,9.65)(11,2.35)

\psline(13,9.65)(14,6.35)
\psline(13,9.65)(12,6.35)

\psline(10,13.65)(9,10.35)
\psline(10,13.65)(13,10.35)
\psline(10,13.65)(6.5,12)(3,6.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

\item{\bf Case $r_{1}=2,r_{2}=1$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,0)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](0,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,0)(-4,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(3.2,-1.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(.2,-2.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{3}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{3}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{5}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^2_{5}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{7}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(1,4){.35}
\rput(1,4){{\footnotesize $u^1_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^2_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(3,8){.35}
\rput(3,8){{\footnotesize $u^1_{3}$}}

\pscircle(9,8){.35}
\rput(9,8){{\footnotesize $u^2_{3}$}}

\pscircle(11,8){.35}
\rput(11,8){{\footnotesize $u^3_{3}$}}

\pscircle(13,8){.35}
\rput(13,8){{\footnotesize $u^4_{3}$}}

\pscircle(9,11){.35}
\rput(9,11){{\footnotesize $u^1_{5}$}}

\pscircle(13,11){.35}
\rput(13,11){{\footnotesize $u^2_{5}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{7}^{1}$}}

\psline(10,13.65)(9,11.35)
\psline(10,13.65)(13,11.35)
\psline(10,13.65)(6,12.5)
\psline(6,12.5)(3,8.35)

\psline(4,.35)(4,1.65)
\psline(6,.35)(4,1.65)

\psline(8,.35)(8,1.65)
\psline(6,.35)(8,1.65)
\psline(10,.35)(8,1.65)

\psline(10,.35)(10,1.65)

\psline(14,.35)(14,1.65)
\psline(16,.35)(14,1.65)
\psline(12,.35)(14,1.65)

\psline(1,3.65)(0,.35)
\psline(1,3.65)(2,.35)

\psline(5,3.65)(4,2.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)

\psline(13,3.65)(14,2.35)

\psline(3,7.65)(1,4.35)
\psline(3,7.65)(5,4.35)

\psline(9,7.65)(9,4.35)

\psline(11,7.65)(12,.35)
\psline(11,7.65)(10,2.35)
\psline(11,7.65)(13,4.35)

\psline(13,7.65)(13,4.35)

\psline(9,10.65)(9,8.35)
\psline(9,10.65)(5,4.35)

\psline(13,10.65)(11,8.35)
\psline(13,10.65)(13,8.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\vspace{2cm}

\newpage

Let $w=s_{1}s_{2}s_{3}s_{2}$. In the following table
$$y\in \{zw^{n}|z\in Y(w), n\in \mathbb{N}\}.$$
$\ $\\

{\small
\begin{table}[htbp] \caption{Condition {\bf I5}}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{3}^{3} & s_{2}s_{3}s_{2} & T_{xu}+ C_{u_{1}^{3}}\\\hline
u_{3}^{3} & ys_{1}s_{2}s_{3}s_{2} & T_{xu} + T_{ys_{1}}C_{u_{1}^{3}}\\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item{\bf Case $1<r_{1}<2,r_{2}=1$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,-1)(.5,-.5)
\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,0)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](0,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,0)(-4,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(3.2,-1.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(.2,-2.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{4}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{4}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{6}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^2_{6}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(1,4){.35}
\rput(1,4){{\footnotesize $u^1_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^2_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(1,6){.35}
\rput(1,6){{\footnotesize $u^{1}_{3}$}}

\pscircle(3,8){.35}
\rput(3,8){{\footnotesize $u^1_{4}$}}

\pscircle(9,8){.35}
\rput(9,8){{\footnotesize $u^2_{4}$}}

\pscircle(11,8){.35}
\rput(11,8){{\footnotesize $u^3_{4}$}}

\pscircle(13,8){.35}
\rput(13,8){{\footnotesize $u^4_{4}$}}

\pscircle(9,11){.35}
\rput(9,11){{\footnotesize $u^1_{6}$}}

\pscircle(13,11){.35}
\rput(13,11){{\footnotesize $u^2_{6}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(10,13.65)(9,11.35)
\psline(10,13.65)(13,11.35)
\psline(10,13.65)(6,12.5)
\psline(6,12.5)(3,8.35)

\psline(4,.35)(4,1.65)
\psline(8,.35)(8,1.65)
\psline(10,.35)(10,1.65)
\psline(14,.35)(14,1.65)

\psline(1,3.65)(0,.35)
\psline(1,3.65)(2,.35)

\psline(5,3.65)(4,2.35)
\psline(5,3.65)(6,.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)
\psline(9,3.65)(6.5,2)(6,.35)

\psline(13,3.65)(12,.35)
\psline(13,3.65)(14,2.35)
\psline(13,3.65)(14.7,2)(16,.35)

\psline(1,5.65)(1,4.35)

\psline(3,7.65)(1,6.35)
\psline(3,7.65)(5,4.35)

\psline(9,7.65)(9,4.35)
\psline(9,7.65)(5,4.35)

\psline(11,7.65)(12,.35)
\psline(11,7.65)(10,2.35)
\psline(11,7.65)(13,4.35)

\psline(13,7.65)(13,4.35)

\psline(9,10.65)(9,8.35)

\psline(13,10.65)(11,8.35)
\psline(13,10.65)(13,8.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

$\ $\\
\newpage

Let $w=s_{1}s_{3}s_{2}s_{1}s_{3}s_{2}$ and $w_{1}=s_{1}s_{2}s_{3}s_{2}$. In the following table
$$y\in \{zw^{n}|z\in Y(w), n\in \mathbb{N}\} \text{ and } y_{1}\in \{zw_{1}^{n}|z\in Y(w_{1}), n\in \mathbb{N}\}$$

{\small
\begin{table}[htbp] \caption{Condition {\bf I5}}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{2}^{1} & s_{1}s_{2} & T_{xu} +v^{a-c}\hspace{2pt} C_{u_{0}^{1}}\\\hline
u_{2}^{1} & ys_{1}s_{3}s_{2} & T_{xu} +v^{a-c}\hspace{2pt} T_{ys_{3}}C_{u_{0}^{1}}\\\hline
u_{4}^{3} & s_{2}s_{3}s_{2} & T_{xu}+v^{-a+2c}\hspace{2pt} C_{u_{1}^{3}}\\\hline
u_{4}^{3} & y_{1}w_{1} & T_{xu} +v^{-a+2c}\hspace{2pt} T_{ys_{1}}C_{u_{1}^{3}}\\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item{\bf Case $(r_{1},r_{2})\in A_{1}$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](-.5,1.5)(0,2)
\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,1)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](0,2)(1,3)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](1,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,1)(-2,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(1.2,.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{3}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{3}}$}}

\rput(-.2,1.5){{\small $ {\bf \tilde{c}^1_{4}}$}}

\rput(-.5,1.2){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{6}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^2_{6}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(1,2){.35}
\rput(1,2){{\footnotesize $u^1_{1}$}}

\pscircle(5,2){.35}
\rput(5,2){{\footnotesize $u^2_{1}$}}

\pscircle(9,2){.35}
\rput(9,2){{\footnotesize $u^3_{1}$}}

\pscircle(13,2){.35}
\rput(13,2){{\footnotesize $u^4_{1}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^1_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^2_{2}$}}

\pscircle(10.5,4){.35}
\rput(10.5,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(5,7){.35}
\rput(5,7){{\footnotesize $u^1_{3}$}}

\pscircle(8.5,7){.35}
\rput(8.5,7){{\footnotesize $u^2_{3}$}}

\pscircle(10.5,7){.35}
\rput(10.5,7){{\footnotesize $u^3_{3}$}}

\pscircle(13,7){.35}
\rput(13,7){{\footnotesize $u^4_{3}$}}

\pscircle(9.5,6){.35}
\rput(9.5,6){{\footnotesize $u^{1}_{4}$}}

\pscircle(10,9){.35}
\rput(10,9){{\footnotesize $u^{1}_{5}$}}

\pscircle(8.5,11){.35}
\rput(8.5,11){{\footnotesize $u^1_{6}$}}

\pscircle(11.5,11){.35}
\rput(11.5,11){{\footnotesize $u^2_{6}$}}

\pscircle(8.5,12.5){.35}
\rput(8.5,12.5){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(10,13.65)(8.5,12.85)
\psline(10,13.65)(11.5,11.35)
\psline(10,13.65)(6.5,12.5)(5,7.35)

\psline(10.5,3.65)(10,.35)

\psline(9.5,5.65)(10.5,4.35)

\psline(1,1.65)(0,.35)
\psline(1,1.65)(2,.35)

\psline(5,1.65)(4,.35)
\psline(5,1.65)(6,.35)

\psline(9,1.65)(10,.35)
\psline(9,1.65)(8,.35)
\psline(9,1.65)(6,.35)

\psline(13,1.65)(14,.35)
\psline(13,1.65)(12,.35)
\psline(13,1.65)(16,.35)

\psline(5,3.65)(5,2.35)

\psline(9,3.65)(9,2.35)

\psline(13,3.65)(13,2.35)

\psline(5,6.65)(1,2.35)
\psline(5,6.65)(5,4.35)

\psline(8.5,6.65)(9,4.35)

\psline(13,6.65)(13,4.35)

\psline(10,8.65)(9.5,6.35)
\psline(10,8.65)(10.5,7.35)

\psline(10.5,6.65)(10.5,4.35)
\psline(10.5,6.65)(12,.35)

\psline(8.5,10.65)(9.5,6.35)
\psline(8.5,10.65)(8.5,7.35)

\psline(11.5,10.65)(10,9.35)
\psline(11.5,10.65)(13,7.35)

\psline(8.5,12.15)(8.5,11.35)
\psline(8.5,12.15)(5,4.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

\item{\bf Case $r_{1}-r_{2}-2=0$, $r_{2}<1$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,1)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](0,2)(1,3)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](1,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,1)(-2,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(1.2,.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{3}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{3}}$}}

\rput(-.5,1.2){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{6}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^2_{6}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](1,2){.35}
\rput(1,2){{\footnotesize $u^1_{1}$}}

\pscircle(5,2){.35}
\rput(5,2){{\footnotesize $u^2_{1}$}}

\pscircle(9,2){.35}
\rput(9,2){{\footnotesize $u^3_{1}$}}

\pscircle(13,2){.35}
\rput(13,2){{\footnotesize $u^4_{1}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](5,4){.35}
\rput(5,4){{\footnotesize $u^1_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^2_{2}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](10.5,4){.35}
\rput(10.5,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(5,7){.35}
\rput(5,7){{\footnotesize $u^1_{3}$}}

\pscircle(8.5,7){.35}
\rput(8.5,7){{\footnotesize $u^2_{3}$}}

\pscircle(10.5,7){.35}
\rput(10.5,7){{\footnotesize $u^3_{3}$}}

\pscircle(13,7){.35}
\rput(13,7){{\footnotesize $u^4_{3}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](10,9){.35}
\rput(10,9){{\footnotesize $u^{1}_{5}$}}

\pscircle(8.5,11){.35}
\rput(8.5,11){{\footnotesize $u^1_{6}$}}

\pscircle(11.5,11){.35}
\rput(11.5,11){{\footnotesize $u^2_{6}$}}

\pscircle(8.5,12.5){.35}
\rput(8.5,12.5){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(10,13.65)(8.5,12.85)
\psline(10,13.65)(11.5,11.35)
\psline(10,13.65)(6.5,12.5)(5,7.35)

\psline(10.5,3.65)(10,.35)

\psline(1,1.65)(0,.35)
\psline(1,1.65)(2,.35)

\psline(5,1.65)(4,.35)
\psline(5,1.65)(6,.35)

\psline(9,1.65)(10,.35)
\psline(9,1.65)(8,.35)
\psline(9,1.65)(6,.35)

\psline(13,1.65)(14,.35)
\psline(13,1.65)(12,.35)
\psline(13,1.65)(16,.35)

\psline(5,3.65)(5,2.35)

\psline(9,3.65)(9,2.35)

\psline(13,3.65)(13,2.35)

\psline(5,6.65)(1,2.35)
\psline(5,6.65)(5,4.35)

\psline(8.5,6.65)(9,4.35)

\psline(13,6.65)(13,4.35)

\psline(10,8.65)(10.5,7.35)

\psline(10.5,6.65)(10.5,4.35)
\psline(10.5,6.65)(12,.35)

\psline(8.5,10.65)(10.5,4.35)
\psline(8.5,10.65)(8.5,7.35)

\psline(11.5,10.65)(10,9.35)
\psline(11.5,10.65)(13,7.35)

\psline(8.5,12.15)(8.5,11.35)
\psline(8.5,12.15)(5,4.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

\item{\bf Case $(r_{1},r_{2})\in A_{2}$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](-1,0)(-2,0)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,1)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](0,2)(1,3)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](1,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,1)(-2,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(2.2,-.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(.5,2.2){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-1.2,.5){{\small $ {\bf \tilde{c}^3_{3}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(-1.8,2.5){{\small $ {\bf \tilde{c}^3_{4}}$}}
\rput(-1.8,-1.5){{\small $ {\bf \tilde{c}^4_{4}}$}}

\rput(-.5,1.2){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{6}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^2_{6}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](1,2){.35}
\rput(1,2){{\footnotesize $u^1_{1}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^2_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^3_{1}$}}

\pscircle(13,2){.35}
\rput(13,2){{\footnotesize $u^4_{1}$}}

\pscircle(6,2){.35}
\rput(6,2){{\footnotesize $u^1_{2}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^2_{2}$}}

\pscircle(11,2){.35}
\rput(11,2){{\footnotesize $u^3_{2}$}}

\pscircle(15,2){.35}
\rput(15,2){{\footnotesize $u^4_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^1_{3}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^2_{3}$}}

\pscircle(14,4){.35}
\rput(14,4){{\footnotesize $u^3_{3}$}}

\pscircle(3,6){.35}
\rput(3,6){{\footnotesize $u^{1}_{4}$}}

\pscircle(9,6){.35}
\rput(9,6){{\footnotesize $u^{2}_{4}$}}

\pscircle(12,6){.35}
\rput(12,6){{\footnotesize $u^{3}_{4}$}}

\pscircle(14,6){.35}
\rput(14,6){{\footnotesize $u^{4}_{4}$}}

\pscircle(12,8){.35}
\rput(12,8){{\footnotesize $u^{1}_{5}$}}

\pscircle(9,10){.35}
\rput(9,10){{\footnotesize $u^1_{6}$}}

\pscircle(13,10){.35}
\rput(13,10){{\footnotesize $u^2_{6}$}}

\pscircle(8,12){.35}
\rput(8,12){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(1,1.65)(0,.35)
\psline(1,1.65)(2,.35)

\psline(4,1.65)(4,.35)
\psline(4,1.65)(6,.35)

\psline(8,1.65)(8,.35)
\psline(8,1.65)(10,.35)
\psline(8,1.65)(6,.35)

\psline(13,1.65)(12,.35)
\psline(13,1.65)(14,.35)
\psline(13,1.65)(16,.35)

\psline(6,1.65)(4,.35)
\psline(6,1.65)(6,.35)

\psline(10,1.65)(8,.35)
\psline(10,1.65)(10,.35)
\psline(10,1.65)(6,.35)

\psline(11,1.65)(10,.35)

\psline(15,1.65)(12,.35)
\psline(15,1.65)(14,.35)
\psline(15,1.65)(16,.35)

\psline(5,3.65)(4,2.35)
\psline(5,3.65)(6,2.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)

\psline(14,3.65)(13,2.35)
\psline(14,3.65)(15,2.35)

\psline(3,5.65)(1,2.35)
\psline(3,5.65)(5,4.35)

\psline(9,5.65)(9,4.35)

\psline(12,5.65)(11,2.35)
\psline(12,5.65)(12,.35)

\psline(14,5.65)(14,4.35)

\psline(12,7.65)(12,6.35)

\psline(9,9.65)(9,6.35)
\psline(9,9.65)(11,2.35)

\psline(13,9.65)(14,6.35)
\psline(13,9.65)(12,8.35)

\psline(8,11.65)(9,10.35)
\psline(8,11.65)(5,4.35)

\psline(10,13.65)(8,12.35)
\psline(10,13.65)(13,10.35)
\psline(10,13.65)(6.5,12)(3,6.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

Let $w_{1}=s_{1}s_{2}s_{3}s_{2}$. In the following table
$$y_{1}\in \{zw^{n}|z\in Y(w_{1}), n\in \mathbb{N}\} $$
{\small
\begin{table}[htbp] \caption{Condition {\bf I5} }
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{4}^{3} & s_{2}s_{3}s_{2} & T_{xu}+v^{-a+2b}\hspace{2pt} C_{u_{2}^{3}}\\\hline
u_{4}^{3} & y_{1}w_{1} & T_{xu} +v^{-a+2b}\hspace{2pt} T_{y_{1}s_{1}}C_{u_{2}^{3}}\\\hline

 \end{array}$
\end{center}
\end{table}}

$\ $\\

\newpage

\item{\bf Case $r_{1}+r_{2}-2=0, r_{1}-r_{2}>1$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](-1,0)(-2,0)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,1)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](0,2)(1,3)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](1,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,1)(-2,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(2.2,-.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(.5,2.2){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-1.2,.5){{\small $ {\bf \tilde{c}^3_{3}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(-1.8,2.5){{\small $ {\bf \tilde{c}^3_{4}}$}}
\rput(-1.8,-1.5){{\small $ {\bf \tilde{c}^4_{4}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{6}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^2_{6}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle[fillstyle=solid,fillcolor=lightgray](1,2){.35}
\rput(1,2){{\footnotesize $u^1_{1}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^2_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^3_{1}$}}

\pscircle(13,2){.35}
\rput(13,2){{\footnotesize $u^4_{1}$}}

\pscircle(6,2){.35}
\rput(6,2){{\footnotesize $u^1_{2}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^2_{2}$}}

\pscircle(11,2){.35}
\rput(11,2){{\footnotesize $u^3_{2}$}}

\pscircle(15,2){.35}
\rput(15,2){{\footnotesize $u^4_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^1_{3}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^2_{3}$}}

\pscircle(14,4){.35}
\rput(14,4){{\footnotesize $u^3_{3}$}}

\pscircle(3,6){.35}
\rput(3,6){{\footnotesize $u^{1}_{4}$}}

\pscircle(9,6){.35}
\rput(9,6){{\footnotesize $u^{2}_{4}$}}

\pscircle(12,6){.35}
\rput(12,6){{\footnotesize $u^{3}_{4}$}}

\pscircle(14,6){.35}
\rput(14,6){{\footnotesize $u^{4}_{4}$}}

\pscircle(9,10){.35}
\rput(9,10){{\footnotesize $u^1_{6}$}}

\pscircle(13,10){.35}
\rput(13,10){{\footnotesize $u^2_{6}$}}

\pscircle(8,12){.35}
\rput(8,12){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(1,1.65)(0,.35)
\psline(1,1.65)(2,.35)

\psline(4,1.65)(4,.35)
\psline(4,1.65)(6,.35)

\psline(8,1.65)(8,.35)
\psline(8,1.65)(10,.35)
\psline(8,1.65)(6,.35)

\psline(13,1.65)(12,.35)
\psline(13,1.65)(14,.35)
\psline(13,1.65)(16,.35)

\psline(6,1.65)(4,.35)
\psline(6,1.65)(6,.35)

\psline(10,1.65)(8,.35)
\psline(10,1.65)(10,.35)
\psline(10,1.65)(6,.35)

\psline(11,1.65)(10,.35)

\psline(15,1.65)(12,.35)
\psline(15,1.65)(14,.35)
\psline(15,1.65)(16,.35)

\psline(5,3.65)(4,2.35)
\psline(5,3.65)(6,2.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)

\psline(14,3.65)(13,2.35)
\psline(14,3.65)(15,2.35)

\psline(3,5.65)(1,2.35)
\psline(3,5.65)(5,4.35)

\psline(9,5.65)(9,4.35)

\psline(12,5.65)(11,2.35)
\psline(12,5.65)(12,.35)

\psline(14,5.65)(14,4.35)

\psline(9,9.65)(9,6.35)
\psline(9,9.65)(11,2.35)

\psline(13,9.65)(14,6.35)
\psline(13,9.65)(12,6.35)

\psline(8,11.65)(9,10.35)
\psline(8,11.65)(5,4.35)

\psline(10,13.65)(8,12.35)
\psline(10,13.65)(13,10.35)
\psline(10,13.65)(6.5,12)(3,6.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

\item{\bf Case $(r_{1},r_{2})\in A_{3}$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,2)(2,2)

\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](1,0)(1,-1)

\psline[linewidth=.7mm](-2,0)(-1,0)
\psline[linewidth=.7mm](-1,0)(-1,-1)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,1)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](0,2)(1,3)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,1)(-2,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(2.2,-.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(.5,2.2){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-.8,.5){{\small $ {\bf \tilde{c}^3_{3}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(2.2,2.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(-.8,1.5){{\small $ {\bf \tilde{c}^3_{4}}$}}
\rput(-1.8,-1.5){{\small $ {\bf \tilde{c}^4_{4}}$}}

\rput(.5,-.2){{\small $ {\bf \tilde{c}^1_{5}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{5}}$}}
\rput(-.5,-.2){{\small $ {\bf \tilde{c}^3_{5}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{6}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^2_{6}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.62cm}
\begin{pspicture}(0,0)(16,15.5)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(1,2){.35}
\rput(1,2){{\footnotesize $u^1_{1}$}}

\pscircle(6,2){.35}
\rput(6,2){{\footnotesize $u^2_{1}$}}

\pscircle(11,2){.35}
\rput(11,2){{\footnotesize $u^3_{2}$}}

\pscircle(13,2){.35}
\rput(13,2){{\footnotesize $u^4_{1}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{2}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{2}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(15,2){.35}
\rput(15,2){{\footnotesize $u^4_{2}$}}

\pscircle(4,5){.35}
\rput(4,5){{\footnotesize $u^{1}_{3}$}}

\pscircle(8,5){.35}
\rput(8,5){{\footnotesize $u^{2}_{3}$}}

\pscircle(14,5){.35}
\rput(14,5){{\footnotesize $u^{3}_{3}$}}

\pscircle(3,6){.35}
\rput(3,6){{\footnotesize $u^1_{4}$}}

\pscircle(7,6){.35}
\rput(7,6){{\footnotesize $u^2_{4}$}}

\pscircle(11,6){.35}
\rput(11,6){{\footnotesize $u^3_{4}$}}

\pscircle(15,6){.35}
\rput(15,6){{\footnotesize $u^4_{4}$}}

\pscircle(3,8){.35}
\rput(3,8){{\footnotesize $u^{1}_{5}$}}

\pscircle(8,8){.35}
\rput(8,8){{\footnotesize $u^{2}_{5}$}}

\pscircle(15,8){.35}
\rput(15,8){{\footnotesize $u^{3}_{5}$}}

\pscircle(10,10){.35}
\rput(10,10){{\footnotesize $u^1_{6}$}}

\pscircle(13,10){.35}
\rput(13,10){{\footnotesize $u^2_{6}$}}

\pscircle(8,12){.35}
\rput(8,12){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(1,1.65)(0,.35)
\psline(1,1.65)(2,.35)

\psline(6,1.65)(4,.35)
\psline(6,1.65)(6,.35)

\psline(10,1.65)(8,.35)
\psline(10,1.65)(10,.35)
\psline(10,1.65)(6,.35)

\psline(13,1.65)(12,.35)
\psline(13,1.65)(14,.35)
\psline(13,1.65)(16,.35)

\psline(4,1.65)(4,.35)
\psline(4,1.65)(6,.35)
\psline(8,1.65)(8,.35)
\psline(8,1.65)(10,.35)
\psline(8,1.65)(6,.35)
\psline(11,1.65)(10,.35)

\psline(15,1.65)(14,.35)
\psline(15,1.65)(12,.35)
\psline(15,1.65)(16,.35)

\psline(4,4.65)(4,2.35)
\psline(4,4.65)(6,2.35)

\psline(8,4.65)(8,2.35)
\psline(8,4.65)(10,2.35)

\psline(14,4.65)(15,2.35)
\psline(14,4.65)(13,2.35)

\psline(3,5.65)(2,.35)
\psline(3,5.65)(4,2.35)
\psline(3,5.65)(1.7,2)(0,.35)
\psline(7,5.65)(8,2.35)

\psline(11,5.65)(11,2.35)
\psline(11,5.65)(12,.35)

\psline(15,5.65)(15,2.35)

\psline(3,7.65)(1,2.35)
\psline(3,7.65)(3,6.35)
\psline(3,7.65)(4,5.35)

\psline(8,7.65)(7,6.35)
\psline(8,7.65)(8,5.35)

\psline(15,7.65)(15,6.35)
\psline(15,7.65)(14,5.35)

\psline(10,9.65)(8,8.35)
\psline(10,9.65)(11,2.35)

\psline(13,9.65)(11,6.35)
\psline(13,9.65)(15,8.35)

\psline(8,11.65)(10,10.35)
\psline(8,11.65)(4,5.35)

\psline(10,13.65)(8,12.35)
\psline(10,13.65)(6,12.35)(3,8.35)
\psline(10,13.65)(13,10.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}
\newpage

Let $w=s_{2}s_{3}s_{2}s_{1}$. In the following table
$$y\in \{zw^{n}|z\in Y(w), n\in \mathbb{N}\}.$$

{\small
\begin{table}[htbp] \caption{Condition {\bf I5} }
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{4}^{2} & s_{2}s_{1} & T_{xu} -v^{c} C_{u_{0}^{4}}\\\hline
u_{4}^{2} & s_{3}s_{2}s_{1} & T_{xu} -v^{c} T_{s_{3}}C_{u_{0}^{4}}\\\hline
u_{4}^{2} & ys_{2}s_{3}s_{2}s_{1} & T_{xu}+T_{ys_{3}s_{2}s_{3}}C_{u_{0}^{4}} -v^{c} T_{ys_{2}s_{3}}C_{u_{0}^{4}} \\\hline
u_{4}^{4} & s_{2}s_{1} & T_{xu} -v^{c} C_{u_{0}^{1}}\\\hline
u_{4}^{4} & s_{3}s_{2}s_{1} & T_{xu} -v^{c} T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{4}^{4} & ys_{2}s_{3}s_{2}s_{1} & T_{xu}+T_{ys_{3}s_{2}s_{3}}C_{u_{0}^{1}} -v^{c} T_{ys_{2}s_{3}}C_{u_{0}^{1}} \\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item{\bf Case $r_{1}-r_{2}-1=0, r_{1}+r_{2}<2$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,2)(2,2)

\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](1,0)(1,-1)

\psline[linewidth=.7mm](-2,0)(-1,0)
\psline[linewidth=.7mm](-1,0)(-1,-1)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(2.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(.2,-1.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(2.2,2.5){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-.8,1.5){{\small $ {\bf \tilde{c}^3_{3}}$}}
\rput(-1.8,-1.5){{\small $ {\bf \tilde{c}^4_{3}}$}}

\rput(.5,-.2){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(-.5,-.2){{\small $ {\bf \tilde{c}^3_{4}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{5}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^2_{5}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{6}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{7}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.62cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(1,4){.35}
\rput(1,4){{\footnotesize $u^1_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^2_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(3,4){.35}
\rput(3,4){{\footnotesize $u^1_{3}$}}

\pscircle(7,4){.35}
\rput(7,4){{\footnotesize $u^2_{3}$}}

\pscircle(11,4){.35}
\rput(11,4){{\footnotesize $u^3_{3}$}}

\pscircle(15,4){.35}
\rput(15,4){{\footnotesize $u^4_{3}$}}

\pscircle(3,7){.35}
\rput(3,7){{\footnotesize $u^{1}_{4}$}}

\pscircle(8,7){.35}
\rput(8,7){{\footnotesize $u^{2}_{4}$}}

\pscircle(14,7){.35}
\rput(14,7){{\footnotesize $u^{3}_{4}$}}

\pscircle(8,10){.35}
\rput(8,10){{\footnotesize $u^1_{5}$}}

\pscircle(13,10){.35}
\rput(13,10){{\footnotesize $u^2_{5}$}}

\pscircle(8,12){.35}
\rput(8,12){{\footnotesize $u^{1}_{6}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{7}^{1}$}}

\psline(4,1.65)(4,.35)
\psline(4,1.65)(6,.35)

\psline(8,1.65)(8,.35)
\psline(8,1.65)(10,.35)
\psline(8,1.65)(6,.35)

\psline(10,1.65)(10,.35)

\psline(14,1.65)(14,.35)
\psline(14,1.65)(16,.35)
\psline(14,1.65)(12,.35)

\psline(1,3.65)(0,.35)
\psline(1,3.65)(2,.35)

\psline(5,3.65)(4,2.35)
\psline(5,3.65)(6,.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)

\psline(13,3.65)(14,2.35)

\psline(3,3.65)(4,2.35)
\psline(3,3.65)(0,.35)
\psline(3,3.65)(2,.35)

\psline(7,3.65)(8,2.35)
\psline(7,3.65)(10,2.35)
\psline(7,3.65)(6,.35)

\psline(11,3.65)(10,2.35)
\psline(11,3.65)(12,.35)

\psline(15,3.65)(14,2.35)
\psline(15,3.65)(16,.35)

\psline(3,6.65)(1,4.35)
\psline(3,6.65)(3,4.35)
\psline(3,6.65)(5,4.35)

\psline(8,6.65)(7,4.35)
\psline(8,6.65)(9,4.35)

\psline(14,6.65)(15,4.35)
\psline(14,6.65)(13,4.35)

\psline(8,9.65)(8,7.35)

\psline(13,9.65)(14,7.35)
\psline(13,9.65)(11,4.35)

\psline(8,11.65)(8,10.35)
\psline(8,11.65)(5,4.35)

\psline(10,13.65)(8,12.35)
\psline(10,13.65)(13,10.35)
\psline(10,13.65)(5,12)(3,7.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}}. Order $\preceq$ on $U$ }
\end{pspicture}
\end{center}

\newpage

Let $w=s_{2}s_{3}s_{2}s_{1}$. In the following table
$$y\in \{zw^{n}|z\in Y(w), n\in \mathbb{N}\}.$$

{\small
\begin{table}[htbp] \caption{Condition {\bf I5} }
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{3}^{2} & s_{2}s_{1} & T_{xu} -v^{c} C_{u_{0}^{4}}\\\hline
u_{3}^{2} & s_{3}s_{2}s_{1} & T_{xu} -v^{c} T_{s_{3}}C_{u_{0}^{4}}\\\hline
u_{3}^{2} & ys_{2}s_{3}s_{2}s_{1} & T_{xu}+T_{ys_{3}s_{2}s_{3}}C_{u_{0}^{4}} -v^{c} T_{ys_{2}s_{3}}C_{u_{0}^{4}} \\\hline
u_{3}^{4} & s_{2}s_{1} & T_{xu} -v^{c} C_{u_{0}^{1}}\\\hline
u_{3}^{4} & s_{3}s_{2}s_{1} & T_{xu} -v^{c} T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{3}^{4} & ys_{2}s_{3}s_{2}s_{1} & T_{xu}+T_{ys_{3}s_{2}s_{3}}C_{u_{0}^{1}} -v^{c} T_{ys_{2}s_{3}}C_{u_{0}^{1}} \\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item{\bf Case $(r_{1},r_{2})\in A_{4}$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,2)(2,2)

\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](1,0)(1,-1)

\psline[linewidth=.7mm](-2,0)(-1,0)
\psline[linewidth=.7mm](-1,0)(-1,-1)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)

\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\psline[linewidth=.7mm](.5,-.5)(0,-1)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(2.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(.2,-1.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(2.2,2.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(-.8,1.5){{\small $ {\bf \tilde{c}^3_{4}}$}}
\rput(-1.8,-1.5){{\small $ {\bf \tilde{c}^4_{4}}$}}

\rput(.5,-.2){{\small $ {\bf \tilde{c}^1_{5}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{5}}$}}
\rput(-.5,-.2){{\small $ {\bf \tilde{c}^3_{5}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{6}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^2_{6}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

$\ $\\

In the following diagram, the green edges only hold for $a\geq 2c$.

\begin{center}
\psset{unit=.62cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(1,4){.35}
\rput(1,4){{\footnotesize $u^1_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^2_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(1,5){.35}
\rput(1,5){{\footnotesize $u^{1}_{3}$}}

\pscircle(3,4){.35}
\rput(3,4){{\footnotesize $u^1_{4}$}}

\pscircle(7,4){.35}
\rput(7,4){{\footnotesize $u^2_{4}$}}

\pscircle(11,4){.35}
\rput(11,4){{\footnotesize $u^3_{4}$}}

\pscircle(15,4){.35}
\rput(15,4){{\footnotesize $u^4_{4}$}}

\pscircle(3,7){.35}
\rput(3,7){{\footnotesize $u^{1}_{5}$}}

\pscircle(8,7){.35}
\rput(8,7){{\footnotesize $u^{2}_{5}$}}

\pscircle(14,7){.35}
\rput(14,7){{\footnotesize $u^{3}_{5}$}}

\pscircle(8,10){.35}
\rput(8,10){{\footnotesize $u^1_{6}$}}

\pscircle(13,10){.35}
\rput(13,10){{\footnotesize $u^2_{6}$}}

\pscircle(8,12){.35}
\rput(8,12){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(4,1.65)(4,.35)
\psline(8,1.65)(8,.35)
\psline(10,1.65)(10,.35)
\psline(14,1.65)(14,.35)

\psline[linecolor=green](8,1.65)(6,.35)
\psline[linecolor=green](14,1.65)(16,.35)

\psline(1,3.65)(0,.35)
\psline(1,3.65)(2,.35)

\psline(5,3.65)(4,2.35)
\psline(5,3.65)(6,.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)
\psline(9,3.65)(7,2)(6,.35)

\psline(13,3.65)(12,.35)
\psline(13,3.65)(14,2.35)
\psline(13,3.65)(15,2)(16,.35)

\psline(1,4.65)(1,4.35)

\psline(3,3.65)(4,2.35)
\psline(3,3.65)(0,.35)
\psline(3,3.65)(2,.35)
\psline(3,3.65)(5,2)(6,.35)

\psline(7,3.65)(8,2.35)
\psline(7,3.65)(10,2.35)
\psline(7,3.65)(6,.35)

\psline(11,3.65)(10,2.35)
\psline(11,3.65)(12,.35)

\psline(15,3.65)(14,2.35)
\psline(15,3.65)(16,.35)
\psline(15,3.65)(13,2)(12,.35)

\psline(3,6.65)(1,5.35)
\psline(3,6.65)(3,4.35)
\psline(3,6.65)(5,4.35)

\psline(8,6.65)(7,4.35)
\psline(8,6.65)(9,4.35)

\psline(14,6.65)(15,4.35)
\psline(14,6.65)(13,4.35)

\psline(8,9.65)(8,7.35)

\psline(13,9.65)(14,7.35)
\psline(13,9.65)(11,4.35)

\psline(8,11.65)(8,10.35)
\psline(8,11.65)(5,4.35)

\psline(10,13.65)(8,12.35)
\psline(10,13.65)(13,10.35)
\psline(10,13.65)(5,12)(3,7.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1} }Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

Let $w=s_{1}s_{3}s_{2}s_{1}s_{3}s_{2}$ and $w_{1}=s_{2}s_{3}s_{2}$. In the following table
$$y\in \{zw^{n}|z\in Y(w), n\in \mathbb{N}\} \text{ and } y_{1}\in \{zw^{n}|z\in Y(w_{1}), n\in \mathbb{N}\}$$

{\footnotesize
\begin{table}[htbp] \caption{Condition {\bf I5} }
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{2}^{1} & s_{1}s_{2} & T_{xu} +v^{a-c} C_{u_{0}^{1}}\\\hline
u_{2}^{1} & ys_{1}s_{3}s_{2} & T_{xu}+v^{a-c} T_{ys_{3}}C_{u_{0}^{1}} \\\hline
u_{4}^{2} & s_{2}s_{1} & T_{xu} -v^{c} C_{u_{0}^{4}}\\\hline
u_{4}^{2} & s_{3}s_{2}s_{1} & T_{xu} -v^{c} T_{s_{3}}C_{u_{0}^{4}}\\\hline
u_{4}^{2} & y_{1}w_{1} & T_{xu}+T_{y_{1}s_{3}s_{2}s_{3}}C_{u_{0}^{4}} -v^{c} T_{y_{1}s_{2}s_{3}}C_{u_{0}^{4}} \\\hline
u_{4}^{4} & s_{2}s_{1} & T_{xu} -v^{c} C_{u_{0}^{1}}\\\hline
u_{4}^{4} & s_{3}s_{2}s_{1} & T_{xu} -v^{c} T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{4}^{4} & y_{1}w_{1}& T_{xu}+T_{y_{1}s_{3}s_{2}s_{3}}C_{u_{0}^{1}} -v^{c} T_{y_{1}s_{2}s_{3}}C_{u_{0}^{1}} \\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item{\bf Case $r_{1}+r_{2}-2=0, r_{1}-r_{2}<1$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,-1)(.5,-.5)
\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,0)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](0,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,0)(-4,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(3.2,-1.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(.2,-2.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{4}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{4}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{6}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^2_{6}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

$\ $\\

In the following diagram, the green edges only hold for $a\geq 2c$.

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(1,4){.35}
\rput(1,4){{\footnotesize $u^1_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^2_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(1,6){.35}
\rput(1,6){{\footnotesize $u^{1}_{3}$}}

\pscircle(3,8){.35}
\rput(3,8){{\footnotesize $u^1_{4}$}}

\pscircle(9,8){.35}
\rput(9,8){{\footnotesize $u^2_{4}$}}

\pscircle(11,8){.35}
\rput(11,8){{\footnotesize $u^3_{4}$}}

\pscircle(13,8){.35}
\rput(13,8){{\footnotesize $u^4_{4}$}}

\pscircle(9,11){.35}
\rput(9,11){{\footnotesize $u^1_{6}$}}

\pscircle(13,11){.35}
\rput(13,11){{\footnotesize $u^2_{6}$}}

\pscircle(8.5,12.5){.35}
\rput(8.5,12.5){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(10,13.65)(8.85,12.5)
\psline(10,13.65)(13,11.35)
\psline(10,13.65)(6,12.5)
\psline(6,12.5)(3,8.35)

\psline(4,.35)(4,1.65)
\psline(8,.35)(8,1.65)
\psline[linecolor=green,linewidth=.4mm](6,.35)(8,1.65)
\psline(10,.35)(10,1.65)
\psline(14,.35)(14,1.65)
\psline[linecolor=green,linewidth=.4mm](16,.35)(14,1.65)

\psline(1,3.65)(0,.35)
\psline(1,3.65)(2,.35)

\psline(5,3.65)(4,2.35)
\psline(5,3.65)(6,.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)
\psline(9,3.65)(6.5,2)(6,.35)

\psline(13,3.65)(12,.35)
\psline(13,3.65)(14,2.35)
\psline(13,3.65)(14.7,2)(16,.35)

\psline(1,5.65)(1,4.35)

\psline(3,7.65)(1,6.35)
\psline(3,7.65)(5,4.35)

\psline(9,7.65)(9,4.35)

\psline(11,7.65)(12,.35)
\psline(11,7.65)(10,2.35)

\psline(13,7.65)(13,4.35)

\psline(9,10.65)(9,8.35)

\psline(13,10.65)(11,8.35)
\psline(13,10.65)(13,8.35)

\psline(8.5,12.15)(9,11.35)
\psline(8.5,12.15)(5,4.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage
Let $w=s_{1}s_{3}s_{2}s_{1}s_{3}s_{2}$. In the following table
$$y\in \{zw^{n}|z\in Y(w), n\in \mathbb{N}\}.$$

{\small
\begin{table}[htbp] \caption{Condition {\bf I5} }
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{2}^{1} & s_{1}s_{2} & T_{xu} +v^{a-c}\hspace{2pt} C_{u_{0}^{1}}\\\hline
u_{2}^{1} & ys_{1}s_{3}s_{2} & T_{xu} +v^{a-c}\hspace{2pt} T_{ys_{3}}C_{u_{0}^{1}}\\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item{\bf Case $(r_{1},r_{2})\in A_{5}$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,-1)(.5,-.5)
\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,0)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](0,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,0)(-4,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(3.2,-1.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(.2,-2.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{4}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{4}}$}}

\rput(-.5,1.2){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{6}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^2_{6}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

$\ $\\

In the following diagram, the green edges only hold for $a\geq 2c$.

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(1,4){.35}
\rput(1,4){{\footnotesize $u^1_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^2_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(1,6){.35}
\rput(1,6){{\footnotesize $u^{1}_{3}$}}

\pscircle(3,8){.35}
\rput(3,8){{\footnotesize $u^1_{4}$}}

\pscircle(9,8){.35}
\rput(9,8){{\footnotesize $u^2_{4}$}}

\pscircle(11,8){.35}
\rput(11,8){{\footnotesize $u^3_{4}$}}

\pscircle(13,8){.35}
\rput(13,8){{\footnotesize $u^4_{4}$}}

\pscircle(11,9.5){.35}
\rput(11,9.5){{\footnotesize $u^{1}_{5}$}}

\pscircle(9,11){.35}
\rput(9,11){{\footnotesize $u^1_{6}$}}

\pscircle(13,11){.35}
\rput(13,11){{\footnotesize $u^2_{6}$}}

\pscircle(8.5,12.5){.35}
\rput(8.5,12.5){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(10,13.65)(8.85,12.5)
\psline(10,13.65)(13,11.35)
\psline(10,13.65)(6,12.5)
\psline(6,12.5)(3,8.35)

\psline(4,.35)(4,1.65)
\psline(8,.35)(8,1.65)
\psline[linecolor=green,linewidth=.4mm](6,.35)(8,1.65)
\psline(10,.35)(10,1.65)
\psline(14,.35)(14,1.65)
\psline[linecolor=green,linewidth=.4mm](16,.35)(14,1.65)

\psline(1,3.65)(0,.35)
\psline(1,3.65)(2,.35)

\psline(5,3.65)(4,2.35)
\psline(5,3.65)(6,.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)
\psline(9,3.65)(6.5,2)(6,.35)

\psline(13,3.65)(12,.35)
\psline(13,3.65)(14,2.35)
\psline(13,3.65)(14.7,2)(16,.35)

\psline(1,5.65)(1,4.35)

\psline(3,7.65)(1,6.35)
\psline(3,7.65)(5,4.35)

\psline(9,7.65)(9,4.35)

\psline(11,7.65)(12,.35)
\psline(11,7.65)(10,2.35)

\psline(13,7.65)(13,4.35)

\psline(11,9.15)(11,8.35)

\psline(9,10.65)(9,8.35)

\psline(13,10.65)(11,9.85)
\psline(13,10.65)(13,8.35)

\psline(8.5,12.15)(9,11.35)
\psline(8.5,12.15)(5,4.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

Let $w=s_{1}s_{3}s_{2}s_{1}s_{3}s_{2}$ and $w_{1}=s_{1}s_{2}s_{3}s_{2}$. In the following table
$$y\in \{zw^{n}|z\in Y(w), n\in \mathbb{N}\} \text{ and } y_{1}\in \{zw_{1}^{n}|z\in Y(w_{1}), n\in \mathbb{N}\}$$

{\small
\begin{table}[htbp] \caption{Condition {\bf I5}}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{2}^{1} & s_{1}s_{2} & T_{xu} +v^{a-c}\hspace{2pt} C_{u_{0}^{1}}\\\hline
u_{2}^{1} & ys_{1}s_{3}s_{2} & T_{xu} +v^{a-c}\hspace{2pt} T_{ys_{3}}C_{u_{0}^{1}}\\\hline
u_{4}^{3} & s_{2}s_{3}s_{2} & T_{xu}+v^{-a+2b}\hspace{2pt} C_{u_{1}^{3}}\\\hline
u_{4}^{3} & y_{1}w_{1} & T_{xu} +v^{-a+2b}\hspace{2pt} T_{y_{1}s_{1}}C_{u_{1}^{3}}\\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item{\bf Case $r_{1}-r_{2}-1=0, r_{1}+r_{2}>2$,  $r_{2}<1$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,0)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](0,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-.5,1.5)(-1,1)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,0)(-4,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(3.2,-1.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(.2,-2.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{3}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{3}}$}}

\rput(-.5,1.2){{\small $ {\bf \tilde{c}^1_{4}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{5}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^2_{5}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{6}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{7}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(1,4){.35}
\rput(1,4){{\footnotesize $u^1_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^2_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(3,8){.35}
\rput(3,8){{\footnotesize $u^1_{3}$}}

\pscircle(9,8){.35}
\rput(9,8){{\footnotesize $u^2_{3}$}}

\pscircle(11,8){.35}
\rput(11,8){{\footnotesize $u^3_{3}$}}

\pscircle(13,8){.35}
\rput(13,8){{\footnotesize $u^4_{3}$}}

\pscircle(11,9.5){.35}
\rput(11,9.5){{\footnotesize $u^{1}_{4}$}}

\pscircle(9,11){.35}
\rput(9,11){{\footnotesize $u^1_{5}$}}

\pscircle(13,11){.35}
\rput(13,11){{\footnotesize $u^2_{5}$}}

\pscircle(8.5,12.5){.35}
\rput(8.5,12.5){{\footnotesize $u^{1}_{6}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{7}^{1}$}}

\psline(10,13.65)(8.85,12.5)
\psline(10,13.65)(13,11.35)
\psline(10,13.65)(6,12.5)
\psline(6,12.5)(3,8.35)

\psline(4,.35)(4,1.65)
\psline(6,.35)(4,1.65)

\psline(8,.35)(8,1.65)
\psline(6,.35)(8,1.65)
\psline(10,.35)(8,1.65)

\psline(10,.35)(10,1.65)

\psline(14,.35)(14,1.65)
\psline(16,.35)(14,1.65)
\psline(12,.35)(14,1.65)

\psline(1,3.65)(0,.35)
\psline(1,3.65)(2,.35)

\psline(5,3.65)(4,2.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)

\psline(13,3.65)(14,2.35)

\psline(3,7.65)(1,4.35)
\psline(3,7.65)(5,4.35)

\psline(9,7.65)(9,4.35)

\psline(11,7.65)(12,.35)
\psline(11,7.65)(10,2.35)

\psline(13,7.65)(13,4.35)

\psline(11,9.15)(11,8.35)

\psline(9,10.65)(9,8.35)

\psline(13,10.65)(11,9.85)
\psline(13,10.65)(13,8.35)

\psline(8.5,12.15)(9,11.35)
\psline(8.5,12.15)(5,4.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

Let $w_{1}=s_{1}s_{2}s_{3}s_{2}$. In the following table
$$ y_{1}\in \{zw_{1}^{n}|z\in Y(w_{1}), n\in \mathbb{N}\}$$

{\small
\begin{table}[htbp] \caption{Condition {\bf I5}}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{3}^{3} & s_{2}s_{3}s_{2} & T_{xu} +v^{b-c}\hspace{2pt} C_{u_{1}^{3}}\\\hline
u_{3}^{3} & y_{1}s_{1}s_{2}s_{3}s_{2} & T_{xu} +v^{b-c}\hspace{2pt} T_{y_{1}s_{1}}C_{u_{1}^{3}}\\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item{\bf Case $(r_{1},r_{2})=(3/2,1/2)$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)
\psline[linewidth=.7mm](1,0)(2,0)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](.5,1.5)(1,1)

\psline[linewidth=.7mm](0,1)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,0)(-4,0)
\psline[linewidth=.7mm](-.5,.5)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(3.2,-1.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(.2,-2.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{3}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{3}}$}}

\rput(.2,1.5){{\small $ {\bf \tilde{c}^1_{5}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^2_{5}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{6}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{7}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(1,4){.35}
\rput(1,4){{\footnotesize $u^1_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^2_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(3,8){.35}
\rput(3,8){{\footnotesize $u^1_{3}$}}

\pscircle(9,8){.35}
\rput(9,8){{\footnotesize $u^2_{3}$}}

\pscircle(11,8){.35}
\rput(11,8){{\footnotesize $u^3_{3}$}}

\pscircle(13,8){.35}
\rput(13,8){{\footnotesize $u^4_{3}$}}

\pscircle(9,11){.35}
\rput(9,11){{\footnotesize $u^1_{5}$}}

\pscircle(13,11){.35}
\rput(13,11){{\footnotesize $u^2_{5}$}}

\pscircle(8.5,12.5){.35}
\rput(8.5,12.5){{\footnotesize $u^{1}_{6}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{7}^{1}$}}

\psline(10,13.65)(8.85,12.5)
\psline(10,13.65)(13,11.35)
\psline(10,13.65)(6,12.5)
\psline(6,12.5)(3,8.35)

\psline(4,.35)(4,1.65)
\psline(6,.35)(4,1.65)

\psline(8,.35)(8,1.65)
\psline(6,.35)(8,1.65)
\psline(10,.35)(8,1.65)

\psline(10,.35)(10,1.65)

\psline(14,.35)(14,1.65)
\psline(16,.35)(14,1.65)
\psline(12,.35)(14,1.65)

\psline(1,3.65)(0,.35)
\psline(1,3.65)(2,.35)

\psline(5,3.65)(4,2.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)

\psline(13,3.65)(14,2.35)

\psline(3,7.65)(1,4.35)
\psline(3,7.65)(5,4.35)

\psline(9,7.65)(9,4.35)

\psline(11,7.65)(12,.35)
\psline(11,7.65)(10,2.35)

\psline(13,7.65)(13,4.35)

\psline(9,10.65)(9,8.35)

\psline(13,10.65)(11,8.35)
\psline(13,10.65)(13,8.35)

\psline(8.5,12.15)(9,11.35)
\psline(8.5,12.15)(5,4.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

\item{\bf Case $r_{1}=1, r_{2}<1$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,2)(2,2)

\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](1,0)(1,-1)

\psline[linewidth=.7mm](-2,0)(-1,0)
\psline[linewidth=.7mm](-1,0)(-1,-1)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,-1)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)

\psline[linewidth=.7mm](.5,.5)(4,-3)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)

\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(2.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,2.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-.8,1.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(.2,-1.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{3}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{3}}$}}

\rput(.5,-.2){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(.2,1.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^3_{4}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{6}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\vspace{2cm}

In the following diagram, the green edges only hold for $a\geq 2c$.

\vspace{1cm}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,12)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(3,4){.35}
\rput(3,4){{\footnotesize $u^1_{2}$}}

\pscircle(7,4){.35}
\rput(7,4){{\footnotesize $u^2_{2}$}}

\pscircle(11,4){.35}
\rput(11,4){{\footnotesize $u^3_{2}$}}

\pscircle(15,4){.35}
\rput(15,4){{\footnotesize $u^4_{2}$}}

\pscircle(1,4){.35}
\rput(1,4){{\footnotesize $u^{1}_{3}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^{2}_{3}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^{3}_{3}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^{4}_{3}$}}

\pscircle(8,8){.35}
\rput(8,8){{\footnotesize $u^{2}_{4}$}}

\pscircle(13,8){.35}
\rput(13,8){{\footnotesize $u^{3}_{4}$}}

\pscircle(3,8){.35}
\rput(3,8){{\footnotesize $u^{1}_{4}$}}

\pscircle(6,9){.35}
\rput(6,9){{\footnotesize $u^{1}_{5}$}}

\pscircle(10,12){.35}
\rput(10,12){{\footnotesize $u_{6}^{1}$}}

\psline(4,1.65)(4,.35)

\psline(8,1.65)(8,.35)
\psline[linecolor=green](8,1.65)(6,.35)

\psline(10,1.65)(10,.35)

\psline(14,1.65)(14,.35)
\psline[linecolor=green](14,1.65)(16,.35)

\psline(3,3.65)(4,2.35)
\psline(3,3.65)(2,.35)
\psline(3,3.65)(0,.35)
\psline(3,3.65)(5,2)(6,.35)

\psline(7,3.65)(8,2.35)
\psline(7,3.65)(6,.35)
\psline(7,3.65)(9,2)(10,.35)

\psline(11,3.65)(10,2.35)
\psline(11,3.65)(12,.35)

\psline(15,3.65)(14,2.35)
\psline(15,3.65)(16,.35)
\psline(15,3.65)(13,2)(12,.35)

\psline(1,3.65)(0,.35)
\psline(1,3.65)(2,.35)
\psline(1,3.65)(4,2.35)

\psline(5,3.65)(4,2.35)
\psline(5,3.65)(6,.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)
\psline(9,3.65)(7.2,2)(6,.35)

\psline(13,3.65)(14,2.35)
\psline(13,3.65)(12,.35)
\psline(13,3.65)(10,2.35)
\psline(13,3.65)(14.7,2)(16,.35)

\psline(3,7.65)(1,4.35)
\psline(3,7.65)(3,4.35)
\psline(3,7.65)(5,4.35)

\psline(8,7.65)(7,4.35)
\psline(8,7.65)(9,4.35)

\psline(13,7.65)(15,4.35)
\psline(13,7.65)(13,4.35)
\psline(13,7.65)(11,4.35)

\psline(6,8.65)(8,8.35)
\psline(6,8.65)(5,4.35)

\psline(10,11.65)(6,9.35)
\psline(10,11.65)(4,9.35)(3,8.35)
\psline(10,11.65)(13,8.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$ }
\end{pspicture}
\end{center}

\newpage

Let $w=s_{1}s_{3}s_{2}s_{1}s_{3}s_{2}$ and $w_{1}=s_{2}s_{3}s_{2}s_{1}$. In the following table
$$y\in \{zw^{n}|z\in Y(w), n\in \mathbb{N}\} \text{ and } y_{1}\in \{zw^{n}|z\in Y(w_{1}), n\in \mathbb{N}\}$$

{\small
\begin{table}[htbp] \caption{Condition {\bf I5}}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{2}^{2} & s_{2}s_{1} & T_{xu} -v^{c} C_{u_{0}^{4}}\\\hline
u_{2}^{2} & s_{3}s_{2}s_{1} & T_{xu} -v^{c} T_{s_{3}}C_{u_{0}^{4}}\\\hline
u_{2}^{2} & y_{1}w_{1} & T_{xu}+T_{y_{1}s_{3}s_{2}s_{3}}C_{u_{0}^{4}} -v^{c} T_{y_{1}s_{2}s_{3}}C_{u_{0}^{4}} \\\hline
u_{2}^{4} & s_{2}s_{1} & T_{xu} -v^{c} C_{u_{0}^{1}}\\\hline
u_{2}^{4} & s_{3}s_{2}s_{1} & T_{xu} -v^{c} T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{4} & ys_{2}s_{3}s_{2}s_{1} & T_{xu}+T_{ys_{3}s_{2}s_{3}}C_{u_{0}^{1}} -v^{c} T_{ys_{2}s_{3}}C_{u_{0}^{1}} \\\hline
u_{3}^{1} & s_{1}s_{2} & T_{xu} +v^{a-c} C_{u_{0}^{1}}\\\hline
u_{3}^{1} & ys_{1}s_{3}s_{2} & T_{xu} +v^{a-c}T_{ys_{3}}C_{u_{0}^{1}}\\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item{Case $(r_{1},r_{2})\in B_{1}$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,2)(2,2)

\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](1,0)(1,-1)

\psline[linewidth=.7mm](-2,0)(-1,0)
\psline[linewidth=.7mm](-1,0)(-1,-1)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,-1)(.5,-.5)
\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](0,0)(1,0)

\psline[linewidth=.7mm](.5,.5)(4,-3)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)

\psline[linewidth=.7mm](1,2)(1,1)

\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)
\psline[linewidth=.7mm](-1,0)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(2.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,2.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-.8,1.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(.2,-1.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{3}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{3}}$}}

\rput(1.2,1.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(-.5,-.2){{\small $ {\bf \tilde{c}^2_{4}}$}}

\rput(.5,-.2){{\small $ {\bf \tilde{c}^1_{5}}$}}
\rput(.2,1.5){{\small $ {\bf \tilde{c}^2_{5}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^3_{5}}$}}

\rput(.5,.2){{\small $ {\bf \tilde{c}^1_{6}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\vspace{2cm}

In the following diagram, the green edges only hold for $a\geq 2c$.

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,15)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(3,4){.35}
\rput(3,4){{\footnotesize $u^1_{2}$}}

\pscircle(7,4){.35}
\rput(7,4){{\footnotesize $u^2_{2}$}}

\pscircle(11,4){.35}
\rput(11,4){{\footnotesize $u^3_{2}$}}

\pscircle(15,4){.35}
\rput(15,4){{\footnotesize $u^4_{2}$}}

\pscircle(1,4){.35}
\rput(1,4){{\footnotesize $u^{1}_{3}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^{2}_{3}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^{3}_{3}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^{4}_{3}$}}

\pscircle(7,5){.35}
\rput(7,5){{\footnotesize $u^1_{4}$}}

\pscircle(15,5){.35}
\rput(15,5){{\footnotesize $u^2_{4}$}}

\pscircle(2,7){.35}
\rput(2,7){{\footnotesize $u^{1}_{5}$}}

\pscircle(8,7){.35}
\rput(8,7){{\footnotesize $u^{2}_{5}$}}

\pscircle(13,7){.35}
\rput(13,7){{\footnotesize $u^{3}_{5}$}}

\pscircle(4,9){.35}
\rput(4,9){{\footnotesize $u^1_{6}$}}

\pscircle(6,9){.35}
\rput(6,9){{\footnotesize $u^{1}_{7}$}}

\pscircle(10,12){.35}
\rput(10,12){{\footnotesize $u_{8}^{1}$}}

\psline(4,1.65)(4,.35)

\psline(8,1.65)(8,.35)
\psline[linecolor=green](8,1.65)(6,.35)

\psline(10,1.65)(10,.35)

\psline(14,1.65)(14,.35)
\psline[linecolor=green](14,1.65)(16,.35)

\psline(3,3.65)(4,2.35)
\psline(3,3.65)(2,.35)
\psline(3,3.65)(0,.35)

\psline(7,3.65)(8,2.35)
\psline(7,3.65)(6,.35)
\psline(7,3.65)(10,2.35)

\psline(11,3.65)(10,2.35)
\psline(11,3.65)(12,.35)

\psline(15,3.65)(14,2.35)
\psline(15,3.65)(16,.35)

\psline(1,3.65)(0,.35)
\psline(1,3.65)(2,.35)
\psline(1,3.65)(4,2.35)

\psline(5,3.65)(4,2.35)
\psline(5,3.65)(6,.35)

\psline(9,3.65)(8,2.35)
\psline(9,3.65)(10,2.35)
\psline(9,3.65)(7.2,2)(6,.35)

\psline(13,3.65)(14,2.35)
\psline(13,3.65)(12,.35)
\psline(13,3.65)(10,2.35)
\psline(13,3.65)(14.7,2)(16,.35)

\psline(7,4.65)(7,4.35)

\psline(15,4.65)(15,4.35)

\psline(2,6.65)(1,4.35)
\psline(2,6.65)(3,4.35)

\psline(8,6.65)(7,5.35)
\psline(8,6.65)(9,4.35)

\psline(13,6.65)(15,5.35)
\psline(13,6.65)(13,4.35)
\psline(13,6.65)(11,4.35)

\psline(4,8.65)(2,7.35)
\psline(4,8.65)(5,4.35)

\psline(6,8.65)(8,7.35)
\psline(6,8.65)(5,4.35)

\psline(10,11.65)(6,9.35)
\psline(10,11.65)(4,9.35)
\psline(10,11.65)(13,7.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$ }
\end{pspicture}
\end{center}

\newpage

Let $w=s_{1}s_{3}s_{2}s_{1}s_{3}s_{2}$ and $w_{1}=s_{2}s_{3}s_{2}s_{1}$. In the following table
$$y\in \{zw^{n}|z\in Y(w), n\in \mathbb{N}\} \text{ and } y_{1}\in \{zw^{n}|z\in Y(w_{1}), n\in \mathbb{N}\} .$$

{\small
\begin{table}[htbp] \caption{Condition {\bf I5} }
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{2}^{2} & s_{2}s_{1} & T_{xu} -v^{c} C_{u_{0}^{4}}\\\hline
u_{2}^{2} & s_{3}s_{2}s_{1} & T_{xu} -v^{c} T_{s_{3}}C_{u_{0}^{4}}\\\hline
u_{2}^{2} & y_{1}w_{1} & T_{xu}+T_{y_{1}s_{3}s_{2}s_{3}}C_{u_{0}^{4}} -v^{c} T_{y_{1}s_{2}s_{3}}C_{u_{0}^{4}} \\\hline
u_{2}^{4} & s_{2}s_{1} & T_{xu} -v^{c} C_{u_{0}^{1}}\\\hline
u_{2}^{4} & s_{3}s_{2}s_{1} & T_{xu} -v^{c} T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{4} & y_{1}w_{1} & T_{xu}+T_{y_{1}s_{3}s_{2}s_{3}}C_{u_{0}^{1}} -v^{c} T_{y_{1}s_{2}s_{3}}C_{u_{0}^{1}} \\\hline
u_{3}^{1} & s_{1}s_{2} & T_{xu} +v^{a-c} C_{u_{0}^{1}}\\\hline
u_{3}^{1} & s_{1}s_{3}s_{2} & T_{xu} +v^{a-c}T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{3}^{1} & s_{2}s_{1}s_{3}s_{2} & T_{xu} +v^{a-c}T_{s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{3}^{1} & s_{3}s_{2}s_{1}s_{3}s_{2} & T_{xu} +v^{a-c}T_{s_{3}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{3}^{1} & s_{1}s_{2}s_{1}s_{3}s_{2} & T_{xu} +v^{a-c}T_{s_{1}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline
u_{3}^{1} & ys_{1}s_{3}s_{2}s_{1}s_{3}s_{2} & T_{xu} +v^{a-c}T_{ys_{1}s_{3}s_{2}s_{3}}C_{u_{0}^{1}}\\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item{\bf Case $r_{1}+r_{2}-1=0$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,2)(2,2)

\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](1,0)(1,-1)

\psline[linewidth=.7mm](-2,0)(-1,0)
\psline[linewidth=.7mm](-1,0)(-1,-1)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(1,0)

\psline[linewidth=.7mm](.5,.5)(4,-3)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](1,2)(3,4)

\psline[linewidth=.7mm](1,2)(1,1)

\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-1,0)(-4,-3)
\psline[linewidth=.7mm](-1,0)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(2.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,2.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-.8,1.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(.2,-1.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{4}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{4}}$}}

\rput(1.2,1.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(-.5,-.2){{\small $ {\bf \tilde{c}^2_{3}}$}}

\rput(.5,.2){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{6}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{7}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

$\ $\\

In the following diagram, the green edges only hold for $a\geq 2c$.

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(4,4){.35}
\rput(4,4){{\footnotesize $u^1_{2}$}}

\pscircle(8,4){.35}
\rput(8,4){{\footnotesize $u^2_{2}$}}

\pscircle(10,4){.35}
\rput(10,4){{\footnotesize $u^3_{2}$}}

\pscircle(14,4){.35}
\rput(14,4){{\footnotesize $u^4_{2}$}}

\pscircle(8,6){.35}
\rput(8,6){{\footnotesize $u^1_{3}$}}

\pscircle(14,6){.35}
\rput(14,6){{\footnotesize $u^2_{3}$}}

\pscircle(2,8){.35}
\rput(2,8){{\footnotesize $u^{1}_{4}$}}

\pscircle(6,8){.35}
\rput(6,8){{\footnotesize $u^{2}_{4}$}}

\pscircle(9,8){.35}
\rput(9,8){{\footnotesize $u^{3}_{4}$}}

\pscircle(12,8){.35}
\rput(12,8){{\footnotesize $u^{4}_{4}$}}

\pscircle(4,12){.35}
\rput(4,12){{\footnotesize $u^{1}_{6}$}}

\pscircle(8,12){.35}
\rput(8,12){{\footnotesize $u_{7}^{1}$}}

\pscircle(8,14){.35}
\rput(8,14){{\footnotesize $u_{8}^{1}$}}

\psline(4,1.65)(4,.35)

\psline(8,1.65)(8,.35)

\psline(10,1.65)(10,.35)

\psline(14,1.65)(14,.35)

\psline(4,3.65)(4,2.35)
\psline(4,3.65)(2,.35)
\psline(4,3.65)(0,.35)

\psline(8,3.65)(8,2.35)
\psline(8,3.65)(10,2.35)
\psline(8,3.65)(6,.35)

\psline(10,3.65)(10,2.35)
\psline(10,3.65)(12,.35)

\psline(14,3.65)(14,2.35)
\psline(14,3.65)(16,.35)

\psline(8,5.65)(8,4.35)

\psline(14,5.65)(14,4.35)

\psline(2,7.65)(0,.35)
\psline(2,7.65)(4,4.35)

\psline(6,7.65)(4,2.35)
\psline(6,7.65)(6,.35)

\psline(9,7.65)(8,6.35)
\psline(9,7.65)(9.5,4)(10,2.35)

\psline(12,7.65)(14,6.35)
\psline(12,7.65)(10,4.35)

\psline(4,11.65)(6,8.35)
\psline(4,11.65)(2,8.35)

\psline(8,11.65)(6,8.35)
\psline(8,11.65)(9,8.35)

\psline(8,13.65)(4,12.35)
\psline(8,13.65)(8,12.35)
\psline(8,13.65)(12,8.35)

\psline[linecolor=green](8,1.65)(6,.35)
\psline[linecolor=green](14,1.65)(16,.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$ }
\end{pspicture}
\end{center}

\newpage

Let $w_{1}=s_{2}s_{3}s_{2}s_{1}$. In the following table
$$y_{1}\in \{zw^{n}|z\in Y(w_{1}), n\in \mathbb{N}\}.$$

{\small
\begin{table}[htbp] \caption{Condition {\bf I5} }
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{2}^{2} & s_{2}s_{1} & T_{xu} -v^{c} C_{u_{0}^{4}}\\\hline
u_{2}^{2} & s_{3}s_{2}s_{1} & T_{xu} -v^{c} T_{s_{3}}C_{u_{0}^{4}}\\\hline
u_{2}^{2} & ys_{2}s_{3}s_{2}s_{1} & T_{xu}+T_{ys_{3}s_{2}s_{3}}C_{u_{0}^{4}} -v^{c} T_{ys_{2}s_{3}}C_{u_{0}^{4}} \\\hline
u_{2}^{4} & s_{2}s_{1} & T_{xu} -v^{c} C_{u_{0}^{1}}\\\hline
u_{2}^{4} & s_{3}s_{2}s_{1} & T_{xu} -v^{c} T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{4} & ys_{2}s_{3}s_{2}s_{1} & T_{xu}+T_{ys_{3}s_{2}s_{3}}C_{u_{0}^{1}} -v^{c} T_{ys_{2}s_{3}}C_{u_{0}^{1}} \\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item{\bf Case $(r_{1},r_{2})\in B_{2}$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,2)(2,2)

\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](1,0)(1,-1)

\psline[linewidth=.7mm](-2,0)(-1,0)
\psline[linewidth=.7mm](-1,0)(-1,-1)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)
\psline[linewidth=.7mm](0,2)(-2,4)

\psline[linewidth=.7mm](1,3)(1,4)
\psline[linewidth=.7mm](1,3)(2,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)
\psline[linewidth=.7mm](-2,0)(-4,-2)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)
\psline[linewidth=.7mm](2,0)(4,-2)

\psline[linewidth=.7mm](0,0)(1,0)

\psline[linewidth=.7mm](.5,.5)(4,-3)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](1,2)(3,4)

\psline[linewidth=.7mm](1,2)(1,1)

\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-1,0)(-4,-3)
\psline[linewidth=.7mm](-1,0)(0,0)

\psline[linewidth=.7mm](1,0)(1,1)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(2.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,3.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-1.8,3.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-2.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,2.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(-.8,1.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,-1.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(.2,-1.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{4}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{4}}$}}

\rput(.8,.5){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(1.2,1.5){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(-.5,-.2){{\small $ {\bf \tilde{c}^2_{3}}$}}

\rput(.5,.2){{\small $ {\bf \tilde{c}^1_{6}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{7}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

$\ $\\

In the following diagram, the green edges only hold for $a\geq 2c$.

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(4,2){.35}
\rput(4,2){{\footnotesize $u^1_{1}$}}

\pscircle(8,2){.35}
\rput(8,2){{\footnotesize $u^2_{1}$}}

\pscircle(10,2){.35}
\rput(10,2){{\footnotesize $u^3_{1}$}}

\pscircle(14,2){.35}
\rput(14,2){{\footnotesize $u^4_{1}$}}

\pscircle(4,4){.35}
\rput(4,4){{\footnotesize $u^1_{2}$}}

\pscircle(8,4){.35}
\rput(8,4){{\footnotesize $u^2_{2}$}}

\pscircle(10,4){.35}
\rput(10,4){{\footnotesize $u^3_{2}$}}

\pscircle(14,4){.35}
\rput(14,4){{\footnotesize $u^4_{2}$}}

\pscircle(8,6){.35}
\rput(8,6){{\footnotesize $u^1_{3}$}}

\pscircle(14,6){.35}
\rput(14,6){{\footnotesize $u^2_{3}$}}

\pscircle(2,8){.35}
\rput(2,8){{\footnotesize $u^{1}_{4}$}}

\pscircle(6,8){.35}
\rput(6,8){{\footnotesize $u^{2}_{4}$}}

\pscircle(9,8){.35}
\rput(9,8){{\footnotesize $u^{3}_{4}$}}

\pscircle(12,8){.35}
\rput(12,8){{\footnotesize $u^{4}_{4}$}}

\pscircle(6,10){.35}
\rput(6,10){{\footnotesize $u^1_{5}$}}

\pscircle(4,12){.35}
\rput(4,12){{\footnotesize $u^{1}_{6}$}}

\pscircle(8,12){.35}
\rput(8,12){{\footnotesize $u_{7}^{1}$}}

\pscircle(8,14){.35}
\rput(8,14){{\footnotesize $u_{8}^{1}$}}

\psline(4,1.65)(4,.35)

\psline(8,1.65)(8,.35)

\psline(10,1.65)(10,.35)

\psline(14,1.65)(14,.35)

\psline(4,3.65)(4,2.35)
\psline(4,3.65)(2,.35)

\psline(8,3.65)(8,2.35)
\psline(8,3.65)(6,.35)

\psline(10,3.65)(10,2.35)
\psline(10,3.65)(12,.35)

\psline(14,3.65)(14,2.35)
\psline(14,3.65)(16,.35)

\psline(8,5.65)(8,4.35)

\psline(14,5.65)(14,4.35)

\psline(2,7.65)(0,.35)
\psline(2,7.65)(4,4.35)

\psline(6,7.65)(4,2.35)
\psline(6,7.65)(6,.35)

\psline(9,7.65)(8,6.35)
\psline(9,7.65)(9.5,4)(10,2.35)

\psline(12,7.65)(14,6.35)
\psline(12,7.65)(10,4.35)

\psline(6,9.65)(6,8.35)

\psline(4,11.65)(6,10.35)
\psline(4,11.65)(2,8.35)

\psline(8,11.65)(6,10.35)
\psline(8,11.65)(9,8.35)

\psline(8,13.65)(4,12.35)
\psline(8,13.65)(8,12.35)
\psline(8,13.65)(12,8.35)

\psline[linecolor=green](8,1.65)(6,.35)
\psline[linecolor=green](14,1.65)(16,.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$ }
\end{pspicture}
\end{center}

\newpage

Let $w_{1}=s_{2}s_{3}s_{2}s_{1}$. In the following table
$$y_{1}\in \{zw_{1}^{n}|z\in Y(w_{1}), n\in \mathbb{N}\}.$$

{\small
\begin{table}[htbp] \caption{Condition {\bf I5}  }
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{2}^{2} & s_{2}s_{1} & T_{xu} -v^{c} C_{u_{0}^{4}}\\\hline
u_{2}^{2} & s_{3}s_{2}s_{1} & T_{xu} -v^{c} T_{s_{3}}C_{u_{0}^{4}}\\\hline
u_{2}^{2} & ys_{2}s_{3}s_{2}s_{1} & T_{xu}+T_{ys_{3}s_{2}s_{3}}C_{u_{0}^{4}} -v^{c} T_{ys_{2}s_{3}}C_{u_{0}^{4}} \\\hline
u_{2}^{4} & s_{2}s_{1} & T_{xu} -v^{c} C_{u_{0}^{1}}\\\hline
u_{2}^{4} & s_{3}s_{2}s_{1} & T_{xu} -v^{c} T_{s_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{4} & ys_{2}s_{3}s_{2}s_{1} & T_{xu}+T_{ys_{3}s_{2}s_{3}}C_{u_{0}^{1}} -v^{c} T_{ys_{2}s_{3}}C_{u_{0}^{1}} \\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item{\bf Case $r_{1}=r_{2}, 1/2<r_{2}<1$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](1,2)(1,3)

\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](1,0)(1,-1)

\psline[linewidth=.7mm](-2,0)(-1,0)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)

\psline[linewidth=.7mm](1,3)(1,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)

\psline[linewidth=.7mm](0,0)(1,0)

\psline[linewidth=.7mm](.5,.5)(4,-3)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](1,2)(3,4)

\psline[linewidth=.7mm](1,2)(1,1)

\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-1,0)(-4,-3)
\psline[linewidth=.7mm](-1,0)(0,0)

\psline[linewidth=.7mm](0,2)(.5,1.5)
\psline[linewidth=.7mm](1,2)(.5,1.5)

\psline[linewidth=.7mm](-1,1)(-.5,.5)
\psline[linewidth=.7mm](-1,0)(-.5,.5)

\psline[linewidth=.7mm](0,-1)(.5,-.5)
\psline[linewidth=.7mm](1,-1)(.5,-.5)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,2.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-.8,1.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-1.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(.2,-1.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(.5,-.2){{\small $ {\bf \tilde{c}^1_{3}}$}}
\rput(.5,1.2){{\small $ {\bf \tilde{c}^2_{3}}$}}
\rput(-.2,.5){{\small $ {\bf \tilde{c}^3_{3}}$}}

\rput(.5,.2){{\small $ {\bf \tilde{c}^1_{4}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{6}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,12)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(3,2){.35}
\rput(3,2){{\footnotesize $u^1_{1}$}}

\pscircle(7,2){.35}
\rput(7,2){{\footnotesize $u^2_{1}$}}

\pscircle(11,2){.35}
\rput(11,2){{\footnotesize $u^3_{1}$}}

\pscircle(15,2){.35}
\rput(15,2){{\footnotesize $u^4_{1}$}}

\pscircle(1,2){.35}
\rput(1,2){{\footnotesize $u^1_{2}$}}

\pscircle(5,2){.35}
\rput(5,2){{\footnotesize $u^2_{2}$}}

\pscircle(9,2){.35}
\rput(9,2){{\footnotesize $u^3_{2}$}}

\pscircle(13,2){.35}
\rput(13,2){{\footnotesize $u^4_{2}$}}

\pscircle(2,4){.35}
\rput(2,4){{\footnotesize $u^1_{3}$}}

\pscircle(8,4){.35}
\rput(8,4){{\footnotesize $u^2_{3}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^3_{3}$}}

\pscircle(3,6){.35}
\rput(3,6){{\footnotesize $u^{1}_{4}$}}

\pscircle(7,6){.35}
\rput(7,6){{\footnotesize $u^1_{5}$}}

\pscircle(10,9){.35}
\rput(10,9){{\footnotesize $u^{1}_{6}$}}

\psline(3,1.65)(2,.35)
\psline(3,1.65)(4,.35)
\psline(3,1.65)(0,.35)

\psline(7,1.65)(6,.35)
\psline(7,1.65)(8,.35)
\psline(7,1.65)(10,.35)

\psline(11,1.65)(10,.35)
\psline(11,1.65)(12,.35)

\psline(15,1.65)(16,.35)
\psline(15,1.65)(14,.35)

\psline(1,1.65)(0,.35)
\psline(1,1.65)(2,.35)
\psline(1,1.65)(4,.35)

\psline(5,1.65)(4,.35)
\psline(5,1.65)(6,.35)

\psline(9,1.65)(10,.35)
\psline(9,1.65)(8,.35)
\psline(9,1.65)(6,.35)

\psline(13,1.65)(12,.35)
\psline(13,1.65)(14,.35)
\psline(13,1.65)(10,.35)
\psline(13,1.65)(16,.35)

\psline(2,3.65)(1,2.35)
\psline(2,3.65)(3,2.35)

\psline(8,3.65)(9,2.35)
\psline(8,3.65)(7,2.35)

\psline(13,3.65)(11,2.35)
\psline(13,3.65)(13,2.35)
\psline(13,3.65)(15,2.35)

\psline(3,5.65)(2,4.35)
\psline(3,5.65)(5,2.35)

\psline(7,5.65)(8,4.35)
\psline(7,5.65)(5,2.35)

\psline(10,8.65)(3,6.35)
\psline(10,8.65)(7,6.35)
\psline(10,8.65)(13,4.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

Let $w=s_{1}s_{3}s_{2}s_{1}s_{3}s_{2}$. In the following table
$$y\in \{zw^{n}|z\in Y(w), n\in \mathbb{N}\}.$$

{\small
\begin{table}[htbp] \caption{Condition {\bf I5}}
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{2}^{1} & s_{1}s_{2} & T_{xu} -+C_{u_{0}^{1}}\\\hline
u_{2}^{1} & ys_{1}s_{3}s_{2} & T_{xu} +T_{ys_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{3} & s_{3}s_{2} & T_{xu} +C_{u_{0}^{6}}\\\hline
u_{2}^{3} & ys_{1}s_{3}s_{2} & T_{xu} +T_{ys_{1}}C_{u_{0}^{6}}\\\hline

 \end{array}$
\end{center}
\end{table}}

\newpage

\item{\bf Case $r_{1}=r_{2}, r_{2}=1/2$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](1,2)(1,3)

\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](1,0)(1,-1)

\psline[linewidth=.7mm](-2,0)(-1,0)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)

\psline[linewidth=.7mm](1,3)(1,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)

\psline[linewidth=.7mm](0,0)(1,0)

\psline[linewidth=.7mm](.5,.5)(4,-3)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](1,2)(3,4)

\psline[linewidth=.7mm](1,2)(1,1)

\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-1,0)(-4,-3)
\psline[linewidth=.7mm](-1,0)(0,0)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,2.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-.8,1.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-1.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(.2,-1.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(.5,.2){{\small $ {\bf \tilde{c}^1_{4}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{6}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,14)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(3,2){.35}
\rput(3,2){{\footnotesize $u^1_{1}$}}

\pscircle(7,2){.35}
\rput(7,2){{\footnotesize $u^2_{1}$}}

\pscircle(11,2){.35}
\rput(11,2){{\footnotesize $u^3_{1}$}}

\pscircle(15,2){.35}
\rput(15,2){{\footnotesize $u^4_{1}$}}

\pscircle(2,4){.35}
\rput(2,4){{\footnotesize $u^1_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^2_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(4,8){.35}
\rput(4,8){{\footnotesize $u^{1}_{4}$}}

\pscircle(7,8){.35}
\rput(7,8){{\footnotesize $u^1_{5}$}}

\pscircle(10,11){.35}
\rput(10,11){{\footnotesize $u^{1}_{6}$}}

\psline(3,1.65)(2,.35)
\psline(3,1.65)(4,.35)
\psline(3,1.65)(0,.35)

\psline(7,1.65)(6,.35)
\psline(7,1.65)(8,.35)
\psline(7,1.65)(10,.35)

\psline(11,1.65)(10,.35)
\psline(11,1.65)(12,.35)

\psline(15,1.65)(16,.35)
\psline(15,1.65)(14,.35)

\psline(2,3.65)(0,.35)
\psline(2,3.65)(3,2.35)

\psline(5,3.65)(4,.35)
\psline(5,3.65)(6,.35)

\psline(9,3.65)(10,.35)
\psline(9,3.65)(7,2.35)

\psline(13,3.65)(11,2.35)
\psline(13,3.65)(15,2.35)

\psline(4,7.65)(2,4.35)
\psline(4,7.65)(5,4.35)

\psline(7,7.65)(5,4.35)
\psline(7,7.65)(9,4.35)

\psline(10,10.65)(7,8.35)
\psline(10,10.65)(4,8.35)
\psline(10,10.65)(13,4.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

$\ $\\
\newpage

\item{\bf Case $r_{1}=r_{2}, 0<r_{2}<1/2$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](1,2)(1,3)

\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](1,0)(1,-1)

\psline[linewidth=.7mm](-2,0)(-1,0)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)

\psline[linewidth=.7mm](1,3)(1,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)

\psline[linewidth=.7mm](0,0)(1,0)

\psline[linewidth=.7mm](.5,.5)(4,-3)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(1,1)
\psline[linewidth=.7mm](1,2)(3,4)

\psline[linewidth=.7mm](1,2)(1,1)

\psline[linewidth=.7mm](0,1)(-3,4)
\psline[linewidth=.7mm](-1,1)(0,1)

\psline[linewidth=.7mm](-1,0)(-4,-3)
\psline[linewidth=.7mm](-1,0)(0,0)

\psline[linewidth=.7mm](1,0)(1,1)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{1}}$}}
\rput(2.2,2.5){{\small $ {\bf \tilde{c}^2_{1}}$}}
\rput(-.8,1.5){{\small $ {\bf \tilde{c}^3_{1}}$}}
\rput(-1.8,-1.5){{\small $ {\bf \tilde{c}^4_{1}}$}}

\rput(.2,-1.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(.8,.5){{\small $ {\bf \tilde{c}^1_{3}}$}}

\rput(.5,.2){{\small $ {\bf \tilde{c}^1_{4}}$}}

\rput(.5,.8){{\small $ {\bf \tilde{c}^1_{5}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{6}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,14)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(3,2){.35}
\rput(3,2){{\footnotesize $u^1_{1}$}}

\pscircle(7,2){.35}
\rput(7,2){{\footnotesize $u^2_{1}$}}

\pscircle(11,2){.35}
\rput(11,2){{\footnotesize $u^3_{1}$}}

\pscircle(15,2){.35}
\rput(15,2){{\footnotesize $u^4_{1}$}}

\pscircle(2,4){.35}
\rput(2,4){{\footnotesize $u^1_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^2_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(5,6){.35}
\rput(5,6){{\footnotesize $u^1_{3}$}}

\pscircle(4,8){.35}
\rput(4,8){{\footnotesize $u^{1}_{4}$}}

\pscircle(7,8){.35}
\rput(7,8){{\footnotesize $u^1_{5}$}}

\pscircle(10,11){.35}
\rput(10,11){{\footnotesize $u^{1}_{6}$}}

\psline(3,1.65)(2,.35)
\psline(3,1.65)(4,.35)

\psline(7,1.65)(6,.35)
\psline(7,1.65)(8,.35)

\psline(11,1.65)(10,.35)
\psline(11,1.65)(12,.35)

\psline(15,1.65)(16,.35)
\psline(15,1.65)(14,.35)

\psline(2,3.65)(0,.35)
\psline(2,3.65)(3,2.35)

\psline(5,3.65)(4,.35)
\psline(5,3.65)(6,.35)

\psline(9,3.65)(10,.35)
\psline(9,3.65)(7,2.35)

\psline(13,3.65)(11,2.35)
\psline(13,3.65)(15,2.35)

\psline(5,5.65)(5,4.35)

\psline(4,7.65)(2,4.35)
\psline(4,7.65)(5,6.35)

\psline(7,7.65)(5,6.35)
\psline(7,7.65)(9,4.35)

\psline(10,10.65)(7,8.35)
\psline(10,10.65)(4,8.35)
\psline(10,10.65)(13,4.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}

\newpage

\item{\bf Case $r_{1}=r_{2}=1$}
$\ $\\

\begin{center}
\begin{pspicture}(-4,-4)(4,4)

\psline[linewidth=.7mm](1,2)(1,3)
\psline[linewidth=.7mm](1,0)(2,0)
\psline[linewidth=.7mm](-1,0)(-2,0)

\psline[linewidth=.7mm](0,-1)(.5,-.5)

\psline[linewidth=.7mm](0,1)(0,2)

\psline[linewidth=.7mm](0,0)(0,1)
\psline[linewidth=.7mm](0.5,0.5)(0,0)

\psline[linewidth=.7mm](0,0)(0,-4)
\psline[linewidth=.7mm](0,0)(-4,-4)

\psline[linewidth=.7mm](0,2)(0,4)

\psline[linewidth=.7mm](1,3)(1,4)

\psline[linewidth=.7mm](1,1)(4,1)
\psline[linewidth=.7mm](1,1)(4,4)

\psline[linewidth=.7mm](-1,1)(-4,1)
\psline[linewidth=.7mm](-1,1)(-4,4)

\psline[linewidth=.7mm](-2,0)(-4,0)

\psline[linewidth=.7mm](1,-1)(1,-4)
\psline[linewidth=.7mm](1,-1)(4,-4)

\psline[linewidth=.7mm](2,0)(4,0)

\psline[linewidth=.7mm](.5,-.5)(1,-1)
\psline[linewidth=.7mm](.5,.5)(4,-3)

\psline[linewidth=.7mm](.5,.5)(1,1)
\psline[linewidth=.7mm](0,1)(.5,.5)
\psline[linewidth=.7mm](.5,1.5)(3,4)
\psline[linewidth=.7mm](.5,1.5)(0,2)

\psline[linewidth=.7mm](.5,1.5)(0,2)
\psline[linewidth=.7mm](0,1)(-3,4)

\psline[linewidth=.7mm](-.5,.5)(-1,1)
\psline[linewidth=.7mm](-.5,.5)(-4,-3)

\rput(-.8,-2.5){{\small $ {\bf \tilde{c}^1_{0}}$}}
\rput(1.8,-2.5){{\small $ {\bf \tilde{c}^2_{0}}$}}
\rput(3.2,-.5){{\small $ {\bf \tilde{c}^3_{0}}$}}
\rput(3.2,2.5){{\small $ {\bf \tilde{c}^4_{0}}$}}
\rput(1.2,3.5){{\small $ {\bf \tilde{c}^5_{0}}$}}
\rput(-.8,3.5){{\small $ {\bf \tilde{c}^6_{0}}$}}
\rput(-2.8,1.5){{\small $ {\bf \tilde{c}^7_{0}}$}}
\rput(-3.2,-.5){{\small $ {\bf \tilde{c}^8_{0}}$}}

\rput(.2,-1.5){{\small $ {\bf \tilde{c}^1_{2}}$}}
\rput(2.2,.5){{\small $ {\bf \tilde{c}^2_{2}}$}}
\rput(.2,2.5){{\small $ {\bf \tilde{c}^3_{2}}$}}
\rput(-1.8,.5){{\small $ {\bf \tilde{c}^4_{2}}$}}

\rput(.2,-.5){{\small $ {\bf \tilde{c}^1_{3}}$}}

\rput(1.2,-.5){{\small $ {\bf \tilde{c}^1_{4}}$}}
\rput(1.2,1.5){{\small $ {\bf \tilde{c}^2_{4}}$}}
\rput(-1.2,1.5){{\small $ {\bf \tilde{c}^3_{4}}$}}
\rput(-1.2,-.5){{\small $ {\bf \tilde{c}^4_{4}}$}}

\rput(.2,.5){{\small $ {\bf \tilde{c}^1_{8}}$}}

\multido{\nx=-4+1}{9}{
\psline(\nx,-4)(\nx,4)}

\multido{\ny=-4+1}{9}{
\psline(-4,\ny)(4,\ny)}

\psline(-4,-3)(-3,-4)
\psline(-3,-3)(-2,-4)
\psline(-2,-3)(-1,-4)
\psline(-1,-3)(-0,-4)
\psline(0,-3)(1,-4)
\psline(1,-3)(2,-4)
\psline(2,-3)(3,-4)
\psline(3,-3)(4,-4)

\psline(-4,-2)(-3,-3)
\psline(-3,-2)(-2,-3)
\psline(-2,-2)(-1,-3)
\psline(-1,-2)(-0,-3)
\psline(0,-2)(1,-3)
\psline(1,-2)(2,-3)
\psline(2,-2)(3,-3)
\psline(3,-2)(4,-3)

\psline(-4,-1)(-3,-2)
\psline(-3,-1)(-2,-2)
\psline(-2,-1)(-1,-2)
\psline(-1,-1)(-0,-2)
\psline(0,-1)(1,-2)
\psline(1,-1)(2,-2)
\psline(2,-1)(3,-2)
\psline(3,-1)(4,-2)

\psline(-4,0)(-3,-1)
\psline(-3,0)(-2,-1)
\psline(-2,0)(-1,-1)
\psline(-1,0)(-0,-1)
\psline(0,0)(1,-1)
\psline(1,0)(2,-1)
\psline(2,0)(3,-1)
\psline(3,0)(4,-1)

\psline(-4,4)(-3,3)
\psline(-3,4)(-2,3)
\psline(-2,4)(-1,3)
\psline(-1,4)(-0,3)
\psline(0,4)(1,3)
\psline(1,4)(2,3)
\psline(2,4)(3,3)
\psline(3,4)(4,3)

\psline(-4,3)(-3,2)
\psline(-3,3)(-2,2)
\psline(-2,3)(-1,2)
\psline(-1,3)(-0,2)
\psline(0,3)(1,2)
\psline(1,3)(2,2)
\psline(2,3)(3,2)
\psline(3,3)(4,2)

\psline(-4,2)(-3,1)
\psline(-3,2)(-2,1)
\psline(-2,2)(-1,1)
\psline(-1,2)(-0,1)
\psline(0,2)(1,1)
\psline(1,2)(2,1)
\psline(2,2)(3,1)
\psline(3,2)(4,1)

\psline(-4,1)(-3,0)
\psline(-3,1)(-2,0)
\psline(-2,1)(-1,0)
\psline(-1,1)(-0,0)
\psline(0,1)(1,0)
\psline(1,1)(2,0)
\psline(2,1)(3,0)
\psline(3,1)(4,0)

\psline(-4,3)(-3,4)
\psline(-3,3)(-2,4)
\psline(-2,3)(-1,4)
\psline(-1,3)(-0,4)
\psline(0,3)(1,4)
\psline(1,3)(2,4)
\psline(2,3)(3,4)
\psline(3,3)(4,4)

\psline(-4,2)(-3,3)
\psline(-3,2)(-2,3)
\psline(-2,2)(-1,3)
\psline(-1,2)(-0,3)
\psline(0,2)(1,3)
\psline(1,2)(2,3)
\psline(2,2)(3,3)
\psline(3,2)(4,3)

\psline(-4,1)(-3,2)
\psline(-3,1)(-2,2)
\psline(-2,1)(-1,2)
\psline(-1,1)(-0,2)
\psline(0,1)(1,2)
\psline(1,1)(2,2)
\psline(2,1)(3,2)
\psline(3,1)(4,2)

\psline(-4,0)(-3,1)
\psline(-3,0)(-2,1)
\psline(-2,0)(-1,1)
\psline(-1,0)(-0,1)
\psline(0,0)(1,1)
\psline(1,0)(2,1)
\psline(2,0)(3,1)
\psline(3,0)(4,1)

\psline(-4,-1)(-3,0)
\psline(-3,-1)(-2,0)
\psline(-2,-1)(-1,0)
\psline(-1,-1)(-0,0)
\psline(0,-1)(1,0)
\psline(1,-1)(2,0)
\psline(2,-1)(3,0)
\psline(3,-1)(4,0)

\psline(-4,-2)(-3,-1)
\psline(-3,-2)(-2,-1)
\psline(-2,-2)(-1,-1)
\psline(-1,-2)(-0,-1)
\psline(0,-2)(1,-1)
\psline(1,-2)(2,-1)
\psline(2,-2)(3,-1)
\psline(3,-2)(4,-1)

\psline(-4,-3)(-3,-2)
\psline(-3,-3)(-2,-2)
\psline(-2,-3)(-1,-2)
\psline(-1,-3)(-0,-2)
\psline(0,-3)(1,-2)
\psline(1,-3)(2,-2)
\psline(2,-3)(3,-2)
\psline(3,-3)(4,-2)

\psline(-4,-4)(-3,-3)
\psline(-3,-4)(-2,-3)
\psline(-2,-4)(-1,-3)
\psline(-1,-4)(-0,-3)
\psline(0,-4)(1,-3)
\psline(1,-4)(2,-3)
\psline(2,-4)(3,-3)
\psline(3,-4)(4,-3)

\rput(0,-4.5){{\small  {\sc Figure \arabic{b}\addtocounter{b}{1}} Partition of $W$}}

\end{pspicture}

\end{center}

\begin{center}
\psset{unit=.65cm}
\begin{pspicture}(0,0)(16,16)

\pscircle(0,0){.35}
\rput(0,0){{\footnotesize $u^1_{0}$}}

\pscircle(2,0){.35}
\rput(2,0){{\footnotesize $u^2_{0}$}}

\pscircle(4,0){.35}
\rput(4,0){{\footnotesize $u^3_{0}$}}

\pscircle(6,0){.35}
\rput(6,0){{\footnotesize $u^4_{0}$}}

\pscircle(8,0){.35}
\rput(8,0){{\footnotesize $u^5_{0}$}}

\pscircle(10,0){.35}
\rput(10,0){{\footnotesize $u^6_{0}$}}

\pscircle(12,0){.35}
\rput(12,0){{\footnotesize $u^7_{0}$}}

\pscircle(14,0){.35}
\rput(14,0){{\footnotesize $u^8_{0}$}}

\pscircle(16,0){.35}
\rput(16,0){{\footnotesize $u^1_{0}$}}

\pscircle(1,4){.35}
\rput(1,4){{\footnotesize $u^1_{2}$}}

\pscircle(5,4){.35}
\rput(5,4){{\footnotesize $u^2_{2}$}}

\pscircle(9,4){.35}
\rput(9,4){{\footnotesize $u^3_{2}$}}

\pscircle(13,4){.35}
\rput(13,4){{\footnotesize $u^4_{2}$}}

\pscircle(3,7){.35}
\rput(3,7){{\footnotesize $u^{1}_{4}$}}

\pscircle(7,7){.35}
\rput(7,7){{\footnotesize $u^{2}_{4}$}}

\pscircle(13,7){.35}
\rput(13,7){{\footnotesize $u^{3}_{4}$}}

\pscircle(10,14){.35}
\rput(10,14){{\footnotesize $u_{8}^{1}$}}

\psline(1,3.65)(0,.35)
\psline(1,3.65)(2,.35)
\psline(1,3.65)(4,.35)

\psline(5,3.65)(4,.35)
\psline(5,3.65)(6,.35)

\psline(9,3.65)(8,.35)
\psline(9,3.65)(10,.35)
\psline(9,3.65)(6,.35)

\psline(13,3.65)(12,.35)
\psline(13,3.65)(14,.35)
\psline(13,3.65)(10,.35)
\psline(13,3.65)(16,.35)

\psline(3,6.65)(1,4.35)
\psline(3,6.65)(5,4.35)

\psline(7,6.65)(5,4.35)
\psline(7,6.65)(9,4.35)

\psline(13,6.65)(13,4.35)

\psline(10,13.65)(7,7.35)
\psline(10,13.65)(13,7.35)
\psline(10,13.65)(5,11)(3,7.35)

\rput(8,-1){\textsc{Figure \arabic{b}\addtocounter{b}{1}} Order $\preceq$ on $U$}
\end{pspicture}
\end{center}
$\ $\\

\newpage

Let $w=s_{1}s_{3}s_{2}s_{1}s_{3}s_{2}$. In the following table
$$y\in \{zw^{n}|z\in Y(w), n\in \mathbb{N}\}.$$

{\small
\begin{table}[htbp] \caption{Condition {\bf I5} }
\label{PcG}
\begin{center}
\renewcommand{\arraystretch}{1.4}
$\begin{array}{|c|c|c|} \hline
u\in U & x\in X_{u} & T_{x}C_{u} \mod \mathcal{H}_{<0}\\ \hline
u_{2}^{1} & s_{1}s_{2} & T_{xu} +\hspace{2pt} C_{u_{0}^{1}}\\\hline
u_{2}^{1} & ys_{1}s_{3}s_{2} & T_{xu} +\hspace{2pt} T_{ys_{3}}C_{u_{0}^{1}}\\\hline
u_{2}^{3} & s_{3}s_{2} & T_{xu}+\hspace{2pt} C_{u_{0}^{6}}\\\hline
u_{2}^{3} & ys_{1}s_{3}s_{2} & T_{xu} +\hspace{2pt} T_{ys_{1}}C_{u_{0}^{6}}\\\hline

 \end{array}$
\end{center}
\end{table}}

\end{longlist}

Abstract: In the last section of the paper "Generalized induction of Kazhdan-Lusztig
cells" and in "Kazhdan-Lusztig cells in affine Weyl groups of rank 2" the
author described the partition into Kazhdan-Lusztig cells of the affine Weyl
groups of rank 2 for all choices of parameters. The proof of these results
relies on some explicit computations with GAP. In these notes we give some
details of these computations.