- there exists an I such that A * I = I * A = A, and
- for all A, B and C, (A * B) * C = A * (B * C), and
- for each A there exists an A' such that A * A' = A' * A = I, and
- 4 sometimes you are given that I and A' are unique.

N PATHS + DISTINCT REVERSES 2 2 + 0, namely, S, R 3 2 + 1, namely, SRRSR, RRSRR 4 3 + 3, namely: SRR RSR SRR RSR RRS RSR RSR RR RSR SRR RSR RRS RSR RRS RSR RR SRR RSR RRS RRS RSR RRS RRR SR