Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
A Unification Algorithm for Associative-Commutative Functions
Journal of the ACM (JACM)
Computer experiments with the REVE term rewriting system generator
POPL '83 Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Incremental Construction of Unification Algorithms in Equational Theories
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Rewrite Methods for Clausal and Non-Clausal Theorem Proving
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Deciding Unique Termination of Permutative Rewriting Systems: Choose Your Term Algebra Carefully
Proceedings of the 5th Conference on Automated Deduction
CAAP '83 Proceedings of the 8th Colloquium on Trees in Algebra and Programming
Orderings for term-rewriting systems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Proofs by induction in equational theories with constructors
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
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The well known Knuth and Bendix completion procedure computes a convergent term rewriting system from a given set of equational axioms. This procedure was extended to handle mixed sets of rules and equations in order to deal with axioms that cannot be used as rules without loosing the required termination property. The developed technique requires the termination property of the rules modulo the equations. We describe here an abstract model of computation, assuming the termination property of the set of rules only. We show that two abstract properties, "uniform confluence modulo" and "uniform coherence modulo" are both necessary and sufficient ones to compute with these models. We then give sufficient properties that can be checked on "parallel critical pairs", assuming the rules are left linear. These results allow to deal with sets of axioms including coramutativity, associativity and idempotency.