Proving a language is not regular
There are many ways to solve this. Here are some:


If $L = \{c^m b^n a^n : n&gt;0, m\geq 0\}$ were regular then so would $L \cap b^*a^*$ be.
The words $\{ b^n : n &gt; 0 \}$ are pairwise inequivalent modulo $L$, so $L$ is irregular according to Myhill-Nerode.
The pumping lemma works if you ignore the $c$ part.