Is the following language context free: $L = \{ uxvy \mid u,v,x,y \in \{ 0,1 \}^+, |u| = |v|, u \neq v, |x| = |y|, x \neq y\} $ ?I think that it's not context free but I'm having a hard time proving it. I tried intersecting this language with a regular language (like  $ \ 0^*1^*0^*1^* $ for example) then use the pumping lemma and \ or homomorphisms but I always get a language that is too complicated to characterize and write down. 
Is this strange language context free?
formal languages;context free;pumping lemma;pushdown automata