Given $L_1$ and $L_2$ over some alphabet:
$L_1@L_2 = \{uv \mid u \in L_1 \land v \in L_2 \land |u|=|v|\}$
The question is: if $L_1$ is regular and $L_2$ is context-free, is $L_1@L_2$ context free?
I've been trying to disprove this but to no avail. So I've been thinking to prove this by buiding a PDA but I can't seem to figure this out.