$$ Question $3$

Th

$$ e pumping lemma with length for context$-$free languages $($CFLs$)$ car Let $L$ be a CFL generated by a CFG in CNF with $p$ live productions. Then any word $w$ in $L$ with length $>2^p$ can be broken into five parts

$w=$uvxyz

such that length $(vxy)2p$

length $(x)>0$

length $(v)+$ length $(y)>0$

and such that all the words $u{v}^{n}x{y}^{n}z$ with nin$\{2,3,4,$dots$\}$ are also in the pumping lemma with length to prove that the language.

$L=\{(a{)}^{2n+1}(b{)}^{n+1}(aa{)}^{n+1}|n0\}$

over the alphabet $=\{a,b\}$ is non$-$context$-$free.