The main purpose of this paper is to present a novel application of algebra with a powerful abstract model of computation, called a term rewriting system. A Menger algebra of rank n is a structure consisting a nonempty set together with the \((n+1)\) -ary operation satisfying the superassociativity. This algebra plays a significant role in the study of multiplace functions. Using the concept of term rewriting systems, a specific method for transforming terms, a new notion of an algebraic structure called the Menger algebra of term rewriting systems which is closely related to semigroups, is naturally presented. This allows us to construct two classes of semigroups derived from the algebra of term rewriting systems. Characterizations of idempotency, regularity, and Green’s relations on these two semigroups are also described.
