Termination orderings for associative-commutative rewriting systems
Journal of Symbolic Computation
Journal of Automated Reasoning
Automated reasoning: 33 BASIC research problems
Automated reasoning: 33 BASIC research problems
Handbook of theoretical computer science (vol. B)
Handbook of logic in computer science (vol. 2)
Equational reasoning and term rewriting systems
Handbook of logic in artificial intelligence and logic programming (vol. 1)
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)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Automated Reasoning: Introduction and Applications
Automated Reasoning: Introduction and Applications
A New Method for Proving Termination of AC-Rewrite Systems
Proceedings of the Tenth Conference on Foundations of Software Technology and Theoretical Computer Science
AC Unification Through Order-Sorted AC1 Unification
RTA '91 Proceedings of the 4th International Conference on Rewriting Techniques and Applications
AC-Complete Unification and its Application to Theorem Proving
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Proceedings of the 7th International Conference on Automated Deduction
Basic Paramodulation and Superposition
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Ordered Semantic Hyper-Linking
Journal of Automated Reasoning
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Unfailing completion is a commonly used technique for equational reasoning. For equational problems with associative and commutative functions, unfailing completion often generates a large number of rewrite rules. By comparing it with a ground completion procedure, we show that many of the rewrite rules generated are redundant. A set of consistency constraints is formulated to detect redundant rewrite rules. We propose a new completion algorithm, consistent unfailing completion, in which only consistent rewrite rules are used for critical pair generation and rewriting. Our approach does not need to use flattened terms. Thus it avoids the double exponential worst case complexity of AC unification. It also allows the use of more flexible termination orderings. We present some sufficient conditions for detecting inconsistent rewrite rules. The proposed algorithm is implemented in PROLOG.