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