Is it possible to get positive radius of convergence for composition of two formal power series, if none of them has positive RoC. I get counter example/proof for all other possibilities. But this one I couldn't do.

Take any power series $F=a_1 X+a_2 X^2+\ldots$ with $a_1\not=0$ with radius of convergence $0$ and $G:=F^{-1}$. Then $G$ also has radius of convergence $0$ because otherwise also $F=G^{-1}$ would have a positive radius of convergence. Finally $F\circ G=X$ has $\infty$ as its radius of convergence.
