Multiplication of natural number parameters and equations in a free semigroup

This paper deals with the problem of describing the set M M of all solutions of an equation over a free semigroup S S . The standard way to do this involves the introduction of auxiliary equations containing polynomials in natural number parameters of arbitrarily high degree. Since S S has a solvable word problem, M M must be computable. However, M M cannot necessarily be computed from the standard description of M M . The present paper shows that the only polynomials needed to describe M M are just products of one parameter by a linear combination of some other parameters. The resulting simplification of the standard description of M M clearly can be used to compute M M .