Is $L = a^{n}b^{n+m}c^{m} | n,m \geq 0$ a context free or a recursive language?

Question

My initial thought is that L can't be context free since I can use the pumping lemma. I also don't think a grammar can be generated since it needs to keep track of the number of c's and a's. However, I'm having a hard time coming up with an algorithm for this language.

Answer 1

Here's a hint:

1. Could you make a grammar for $a^nb^n$, $n\ge 0$?
2. Could you make a grammar for $b^mc^m$, $m\ge 0$?
3. Could you make a production that concatenates the languages in (1) and (2) above?