L $=\{$a$^$i b$^$i $|$ i $>=0,$j $>=0\}$

Given m $=4$ and word selection of aabb an xyz can be

selected of $\text{'}$a$\text{'}\text{'}$ab$\text{'}$ and $\text{'}$b$\text{'}.$ Correspondingly I can 'pump' ab to abab making aababb which is not in my language that may suggest non$-$regularity.

What did I prove or not prove $-$ explain your answer as related to what we know about application of p$.$I.