# A context free grammar for the language of even-length non-palindromes [duplicate]

I am trying to find a context free grammar for the language

$L = \{xy \mid |x|=|y| \text{ and } x≠y^R\}$

where $y^R$ is the reverse of string y and $x, y\in \{a,b\}^*$ . Here is a possible solution: $G=\{V,Σ,R,S\}$
where
$V=\{A,B,a,b\}$
$Σ=\{a,b\}$
$R=\{S\rightarrow aSa|bSb|aBb|bBa,$
$\ \ \ \ \ \ \ \ \ \ B\rightarrow aBa|bBb|aBb|bBa\}$

Is this correct?

I found a similar problem here.