My study group and I have had some back and forth on one exercise and I haven't found any matching solution online. The task looks as follows: Prove that $L$ is not regular given
$$ L = \{ a^k b a^{m-1} \mid k,m \in \mathbb{N} \} $$
Questions:
- How does $m-1$ affect my choice of the word to be pumped? There must be a way to rule out $m=0$ because otherwise my length would be negative.
- Would it be wrong to choose $w = a^{n-1}ba^n$ with the intent of pumping down $y = b$?
Every answer is highly appreciated.