listed below, give a complete problem defining the following.

1. State representation 2. Initial state 3. Goal state 4. Actions 5. Path cost

a. You start with the sequence ABABAECCEC, or in general any sequence made from A, B, C, and E. you can transform this sequence using the following equalities: AC = E, AB = BC, BB = E, and Ex = x for any x. for example, ABBC can be transformed into AEC, and then AC, and then E. your goal is to produce the sequence E.