Is the language $L=\{ xyx^Ry^R \mid x,y \text{ is an element of }\{0,1\}^*\}$ context-free?
Note: $x^R$ is the reverse of $x$.
My Work: I think this is a context free language. Since a pushdown automaton (PDA) accepts context-free languages, I am trying to draw a PDA for this language. When I draw a PDA, how does the PDA tell $x$ and $y$ apart? Or is this not a context-free language? (then I can use pumping length to prove this)