Let $L = L_1^* \circ L_2^*$ where $L_1 = \{1^n 0^m 1^n : n,m \in \Bbb N\}$ and $L_2 = \{0^m 1^{2m} : m \in N\}$.
Is the language $L$ a context free language?
I think I can write automata for $L_1$ and $L_2$ but can't really find a way to add the $^*$ and to concatenate together.