Proving that $L=\lbrace{ab^{n}ba^{n}|n\geq1}\rbrace$ is not regular with pumping lemma
It's not sufficient proof because you only proved that if you choose the decomposition $x=ab^q$ and $z$ the rest does not meet the three points of the pumping lemma but remember that the lemma says: 

If $L$ is regular then there is a constant $N&gt;0$ associated to $L$ such that  $\forall \sigma \in L$ with $|\sigma|\geq N$ $\textbf{exist}$ a decomposition $\sigma = xyz$ ... 

Summarizing. you proved that your decomposition doesn't work. Now you have to try all other possible decompositions.