I have the formal language $Z$ over the alphabet $Q \{a, b, c\}$ and it is generated by the context-free grammar whose non-terminals are $S, A$, and $B$, the start symbol is $S$, production rules are as follows:
(1) S → abSb
(2) S → A
(3) A → Bc
(4) B → cA
(5) A → a
The question asked to describe the structure of strings in the language and I came up with $Z = \{w ∈ Q^* | w = ab^n\ o\ u\ o\ b^m, u ∈ Q^*, n, m ∈ N^*\}$. ($o$ means concatenated here).
I am now struggling with the second part of the question where I am asked to show this language isn't regular using the pumping lemma. I understand the concept of the pumping lemma and I have applied to simpler questions but I have never used it for a language involving concatenation.
Most examples I have seen online have been of structure $L = \{0^n 1 0^n 1 | n ∈ N^*\}$. I am wondering if there is some rule I am missing that says the powers must be the same or if I have gone wrong in my definition of the language.
Thanks in advance :)