A decision procedure for the existential theory of term algebras with the Knuth-Bendix ordering

Abstract

The authors show the decidability of the existential theory of term algebras with any Knuth-Bendix ordering. They achieve this by giving a procedure for solving Knuth-Bendix ordering constraints. As for complexity, NP-hardness of the set of satisfiable quantifier-free formulas can be shown in the same way as by R. Nieuwenhuis (1993). The algorithm presented does not give an NP upper bound; we point out parts of our algorithm that may cause nonpolynomial behavior.