# Proving that a specific grammar is ambiguous

How can I prove that the following grammar is ambiguous:

$$A \to AA\mid B \\ B \to aBb\mid ab$$

I tried finding a string that can be derived in two different ways, but to no avail.

## 2 Answers

The word $$ababab$$ can be derived in two different ways.

If you don't see why, I suggest starting with the simpler grammar $$A \to AA|a$$.

• I dont get how you did that – Nnina Apr 11 '19 at 12:19
• I'm afraid you'll have to take it from here. – Yuval Filmus Apr 11 '19 at 12:20

I could suggest a 6-letter word here but that would be too easy.

The productions for $$B$$ do not look promising. So check what can be done with $$A$$. Can you produce the same sequence of 3 non-terminals via 2 different derivations?