# Complete equational unification based on an extension of the Knuth-Bendix completion procedure

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## Abstract

A unifier is a substitution that makes two terms syntactically equal. In this paper, we discuss a more semantical unifier: an equational unifier, which is a substitution that makes two terms equal modulo a congruence relation. As a result we will give a general procedure that enumerates a complete set of equational unifiers for a given pair of terms under a given congruence.

## Keywords

Inference Rule Congruence Relation Critical Pair Ground Term Fairness Condition
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© Springer-Verlag Berlin Heidelberg 1992