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# [Answers] Proving a language is not regular with pumping lemma

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Problem Detail:

I'm having a little bit of an issue with a pumping lemma problem. I've successfully completely all my other problems but this is the last one and I'm a little confused I must say. If anyone can help me out, it'd be much appreciated.

$$A = \{a^n b^m c^l \mid n\leq m \vee m\leq l\}$$

#### Answered By : Luke Mathieson

To expand a little on Ran G.'s comment, given a pumping length of $p$, we can take the string $s=a^{p}b^{p} \in A$, then splitting into $s=xyz$, the $y$ section (the part that can be pumped) must be all $a$s, so pumping up leaves us with a string $s'=a^{p+k}b^{p} \notin A$.