is this a Context free Language : $L=\{W_1W_2 \mid W_1 \ne W_2 \: \text{and} \: |W_1|=|W_2|\}$ [duplicate]

$L=\{W_1W_2 \mid W_1 \ne W_2 \: \text{and} \: |W_1|=|W_2|\}$

Alphabet = { a , b }*

Considering L={WW} is not context free, shouldn't this be non context free as well? otherwise can you provide a machine or grammar which accepts this?

marked as duplicate by Raphael♦Sep 26 '17 at 19:51

This is a classical example of a context-free language whose complement is not context-free. It is context-free since every word in $w$ has the form $$\Sigma^i a \Sigma^j \Sigma^i b \Sigma^j = \Sigma^i a \Sigma^i \Sigma^j b \Sigma^j$$ or the similar form with the locations of $a$ and $b$ switched.