Combination of unification algorithms

Abstract

Unification in equational theories, i.e. solving equations in varieties, is a basic operation in many applications of Computer Science, particularly in Automated Deduction [Si 84]. A combination of unification algorithms for regular finitary collapse free equational theories with disjoint function symbols is presented. The idea is first to replace certain subterms by constants and to unify this constant abstraction and then to handle the replaced subterms in a recursive step. Total correctness is shown, i.e. the algorithm terminates and yields a correct and complete set of unifiers provided the special algorithms do.