I'm trying to prove a language is not regular through using pumping lemma, but can't seem to come up with any way of doing it.
The alphabet is:
$$ \Sigma = \{c, d\} $$
The language is:
$$ A = \{z \in \Sigma^* \mid c(z) > d(z)\} , \text{where $c(w)$ and $d(w)$ means occurrences of $c$ or $d\in z$ }$$
I tried to define a string like so:
Pumping length = P
$$ s = c^{(P+1)}d^P $$
Here is how I tried to solve it:
If we select P = 5. Then s = ccccccddddd and split it in 3 parts. Where x = ccccccd, y = ddd and z = d. (Is that even allowed though as |xy| <= P, but now |xy|=10 and 10>5). If I then do y^2. Then I get s = ccccccdddddddd, so now d>c which proves the string is not in the language. Does this then prove that the language is not regular?