Pumping lemma occurrence of c > d
You need to show that with that arbitrary pumping length $P$, for any partition $c^{(P+1)}d^P = xyz$ such that $|y|&gt;0$ and $|xy|\leq P$, there is some $i$ such that $xy^iz \not\in A$.

Since for any partition we require that $|xy|\leq P$, then $x$ and $y$ necessarily consist only of $c$'s. Also, you know that $|y| &gt;0$ (it's also a requirement). Can you find an $i\in\mathbb{N}$ such that the amount of $c$'s in $xy^iz$ is less than or equal to the amount of $d$'s?