:How to " solve a proof " is a bit vague, but I think you mean to ask how one uses the pumping lemma to show that a given language is " not " regular . ( The pumping lemma doesn't show a language " is " regular; it can only be used to prove that no finite state automaton can accept a particular language, for if one existed, the pumping lemma would apply . ) These lecture notes are decent and provide a number of examples starting at " Applications ".
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