Obtaining Complete Sets of Reductions and Equations Without Using Special Unification Algorithms

Introduction. This report summarizes a critical pairs completion procedure for varieties of abstract algebras whose definition may include non.ofientable identities. More details appear in [3,4]. When successful, the procedure solves the free word problem for the vsxiety. In contrast to previous such procedures it does not require the use of specialized unification algorithms. The offsetting disadvantage is that the coraplete sets produced are often infinite.