Grammar for ${a^n b^n c^{n+m}}$

Problem Detail: 

Can we define a grammar for the following language?

$$L = \{a^n b^n c^{n+m} | n,m>=0\}\,. $$

I can define one for this:
$$L=\{a^nb^n|n,m>=0\} $$

S --> aSb | λ

or this one: $$L=\{b^nc^{n+m}|n,m>=0\} $$

S --> Ac
A --> bSc | Sc | λ

but I can't solve the first one, any hint?

Asked By : Amen

Answered By : d'alar'cop

This gives the language: $L = \{a^n b^n c^n c^m | n,m>=0\}\,. $

1. S → a b c C | N | ε
2. N → a N B c C | a b c
3. c B → W B
4. W B → W X
5. W X → B X
6. B X → B c
7. b B → b b
8. C → cC | ε

Best Answer from StackOverflow

Question Source : http://cs.stackexchange.com/questions/30331