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Is there a context-free but non regular language, which still meets the requirements of the regular pumping lemma?
Regular Pumping Lemma: $\exists n\in \mathbb{N}:\forall w \in L:{\mid w \mid} \geq n: \exists x,y,z\in \Sigma^*$: \begin{align} i)&w=xyz\\ ii)& {\mid y \mid} \geq 1\\ iii)& {\mid xy \mid} \leq n\\ iv)& \forall i\in \mathbb{N_0}:xy^iz\in L \end{align}

Is there any $L$ with $L\in CFL$ and $L\notin REG$ but still meets the regular pumping lemma from above?

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