Suppose we have two context-free Languages $L_{1}$ and $L_{2}$, and we form a new language $L_{3}=L_{1} \circ L_{2} = \{\alpha\beta | \alpha \in L_{1},\beta \in L_{2},|\alpha|=|\beta|\}$. Is it possible that $L_{3}$ is not context-free?
Operation on two CFLs which results in a non-CFL
context free