On ground AC-completion

Abstract

We prove that a canonical set of rules for an equational theory defined by a finite set of ground axioms plus the associativity and commutativity of any number of operators must be finite. As a corollary, we show that ground AC-completion, when using a total AC-simplification ordering and an appropriate control, must terminate. Using a recent result of Narendran and Rusinowitch (in this volume), this implies that the word problem for such a theory is decidable.