# Context Free Grammar $L=\{a^ib^{2i}c^{2i} | i>1\}$

In one of my exams I needed to find a CFG for $$L=\{a^ib^{2i}c^{2i} | i>1\}$$.

however, it really seemed to me that it is not a CFG. I tried to show it is not using the pumping lemma, and think I managed, but I don't really know if I did something wrong there.

So was I wrong or the question is wrong?

Thank you.

Your language is not context-free. You can see this by applying the inverse of the homomorphism which sends $$a$$ to $$a$$, $$b$$ to $$bb$$ and $$c$$ to $$cc$$; this results in the language $$\{a^ib^ic^i : i > 1\}$$, which differs from a well-known non-context-free language by just a finite number of words.