Question

In a language, words are made with only three letters A, B and C. The words follow a fixed sequence.
(1) If X is a viable word sequence ending with A then a B can be added at the end.
(2) If CX is a viable word sequence then so is CXX.
(3) If there are three A’s i.e. AAA then the trio can be replaced by a single B.
(4) If there are two B’s i.e. BB then the pair can be dropped altogether.
It is known that CA is a viable word.
Example: To obtain CBAAB from CA, the minimum number of steps is:
Step 1: CA
Step 2: CAA
Step 3: CAAAA
Step 4: CBA
Step 5: CBAB
Step 6: CBABBAB
Step 7: CBAAB
In one step only one operation can be carried out