An inductive theorem proving method for constrained term rewriting systems, which is based on rewriting induction, needs a decision procedure for reduction-completeness of constrained terms. In addition, the sufficient complete property of constrained term rewriting systems enables us to relax the side conditions of some inference rules in the proving method. These two properties can be reduced...

In this paper we propose a new approach to theorem proving in first-order logic based on the term-rewriting method. First for propositional calculus, we introduce a canonical term-rewriting system for Boolean algebra. This system enables us to transform the first-order predicate calculus into a form of equational logic, and to develop several complete strategies (both clausal and nonclausal) fo...

An important problem in universal algebra consists in finding presentations of algebraic theories by generators and relations, which are as small as possible. Exhibiting lower bounds on the number of those generators and relations for a given theory is a difficult task because it a priori requires considering all possible sets of generators for a theory and no general method exists. In this art...

We design a normalizing strategy for orthogonal term rewriting systems (OTRSs), which is a generalization of the call-by-need strategy of Huet-L evy 4]. The redexes contracted in our strategy are essential in the sense that they have \descendants" under any reduction of a given term. There is an essential redex in any term not in normal form. We further show that contraction of the innermost es...

Monads can be used to model term rewriting systems by generalising the well-known equivalence between universal algebra and monads on the category Set. In [Lü96], this semantics was used to give a purely categorical proof of the modularity of confluence for the disjoint union of term rewriting systems. This paper provides further support for monadic semantics of rewriting by giving a categorica...