How can I show that this language is not regular?
$$ L = \{a^n (ca)^m b^{n+1} \mid m \ge 0 , n \ge 0 \} $$
This is my attempted solution:
Assuming the pumping number to be $p$ and making $m=0$
the language reduces to $a^p b^{p+1}$ so $s=a^p b^{p+1}$
let $s=xyz$ where $y$ is not $\epsilon \\$
$y=a^k$; $0 \lt k<=p$
$x=a^q$; $0 \lt= q \lt p$
$z=a^{p-k-q}b^{n+1}$
so with this definitions, $xyyz$ cannot be part of the language since this would be written as
$xyyz$=$a^qa^ka^ka^{p-k-q}b^{p+1}$ = $a^{k+p}b^{p+1}$ which means there is always an extra $a$ which is not in the original language.
Is this approach correct ?
