Example 1. (x * y) * z = x * (y * z). x * y != x * z | y = z. x * y != z * y | x = z. a * (b * a) = b * (a * b). a * a = b * (b * b). goal: the semigroup is trivial. Example 2. a * (b * a) = b * (a * b). a * (a * a) = (b * b) * (b * b). Example 3. a * (b * a) = b * (a * b). (a * a) * (a * a) = (b * b) * (b * (b * b)). Example 3 generalized a * (b * a) = b * (a * b). a^n = b^(n+1). Example 4. a * b = b * (a * a). b * c = c * (b * b). c * a = a * (c * c). Example 5. (b * b) * a = a * (b * (b * b)). (a * a) * b = b * (a * (a * a)). Example 6. % contributed by Mark Sapir (a * a) * a = b * (b * (b * b)). a * c = c * b. c * b = b * a.