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This question already has an answer here:

When I prove some language is context free, It is too hard to find example string. Is there any tips? It takes too many time or eventually give up.

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marked as duplicate by Evil, xskxzr, Discrete lizard May 23 at 15:44

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ You seem to be asking specifically about applications of the pumping lemma. If so, can you update the question accordingly? $\endgroup$ – Yuval Filmus May 21 at 16:33
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The pumping lemma for CFGs can often be used to show a language is not a CFL.

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