In order to show that $ \{A^nB^nA^nB^n \mid n \geq 0 \}$ isn't CFL, I was trying to use a pumping lemma this way: At first we assign $w= A^jB^jA^jB^j ,$ $(w^i=uv^ixy^iz), p<|vxy|, p<j.$
- if $vy$ contains just $a$s we choose i=0 for $w^i$, so in this case the number of $a$s isn't equal to the $b$s.
- if $vy$ contains just $b$s we choose i=0 for $w^i$, so in this case the number of $b$s isn't equal to $a$s.
- if $vy$ contains both $a$s and $b$s then for any i there will be a difference in there quantity compare to the $n$ $a$s and $b$s that aren't in $vy$. Also $vy$ can't contain the whole world since the number of $a$s larger than $p$.
- Isn't it CFL? Can pumping lemma help here?
I was told in class that it isn't correct to use pumping lemma here, why?