Is this a CFL: $L_1 = \{wxyx | w, x, y \in (0 + 1)^+\}$?
It’s a trick question. There must be four letters or more. Let the last letter be a, where a is 0 or 1. If any other letter other than the first or second to last is a, then the string is in L. (Pick x = a, w = everything before the first a, y = everything between first and last a). If you can’t find a in these places, the string cannot be in the language because you can’t match the last x with another one. 

So you don’t have to check for two equal strings of identical length at all, the language is much simpler. And it is regular.