omplete the proof below that the set L $=\{$akbk$$ncn $|$ k$,$ n $>=1\}$ is not regular.

Proof: Assume $($towards a contradiction$)$ that L is regular. Then the Pumping Lemma

applies to L$.$ Let p be the pumping length of L$.$ Choose w to be the string

Since this string is in L and has length greater than or equal to p$,$ the Pumping Lemma

guarantees w can be divided into parts w $=$ xyz such that for any i $>=0,$ xyiz is in L$,$ and

that $|$y$|>0$ and $|$xy$|<=$ p$.$ But if we let i $=$

we get a string xyiz that is not in L because

This is a contradiction. Therefore the assumption is false, and L is not regular.

$6$