Use the pumping lemma to prove that the following language is not context free
Consider the following Context Free Grammar $G$:

$S \rightarrow aSdd\  |\ X\ |\ \epsilon$
$X \rightarrow bXc\ |\ \epsilon$   

The language $L(G)$ generated by $G$ corresponds to the set of all the strings $\{\epsilon, add, aadddd, ..., bc, bbcc,..., abcdd, abbccdd,...\}$.
More generally, it corresponds to $ \{ a^{n}b^{m}c^{m}d^{2n} | n,m ≥ 0 \}$.