Is this a CFL?$$\{a^n b^m c^k\; : \;k>m \; \; k>n\}$$When on seeing $a$'s and $b$'s I push them onto stack and as I see $ c$ as input if $ TOS$ is $b$ ,I pop them ,again if $TOS$ is a,I pop them so when my $TOS$ of stack is empty and input is$ c $,I do not make any changes in the stack and that clearly implies that i have no of $c$'s to be greater than both $a$ and $b$.But its supoosedly not a CFL. Need help where I'm going wrong in constructing the PDA. Because supposedly a PDA can be made for this which makes it a CFL.
Context free grammar $\{a^n b^m c^k\; : \;k>m \; \; k>n\}$
context free;automata;pushdown automata;context sensitive