An algebraic approach to unification under associativity and commutativity
Proc. of the first international conference on Rewriting techniques and applications
Proof by induction using test sets
Proc. of the 8th international conference on Automated deduction
Artificial Intelligence
Automated Theorem-Proving for Theories with Simplifiers Commutativity, and Associativity
Journal of the ACM (JACM)
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)
Proving termination with multiset orderings
Communications of the ACM
Computer experiments with the REVE term rewriting system generator
POPL '83 Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
On proving inductive properties of abstract data types
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
A Confluence Criterion Based on the Generalised Neman Lemma
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Associative-Commutative Unification
Proceedings of the 7th International Conference on Automated Deduction
RRL: A Rewrite Rule Laboratory
Proceedings of the 8th International Conference on Automated Deduction
Completion of a set of rules modulo a set of equations
POPL '84 Proceedings of the 11th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Abstract Data Type Specification in the Affirm System
IEEE Transactions on Software Engineering
Equational inference, canonical proofs, and proof orderings
Journal of the ACM (JACM)
Experiments with subdivision of search in distributed theorem proving
PASCO '97 Proceedings of the second international symposium on Parallel symbolic computation
Solution of the Robbins Problem
Journal of Automated Reasoning
Fatal steps of Knuth-Bendix completion
Nordic Journal of Computing
A taxonomy of theorem-proving strategies
Artificial intelligence today
AC completion with termination tools
CADE'11 Proceedings of the 23rd international conference on Automated deduction
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
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The Knuth and Bendix test for local confluence of a term rewriting system involves generating superpositions of the left-hand sides, and for each superposition deriving a critical pair of terms and checking whether these terms reduce to the same term. We prove that certain superpositions, which are called composite because they can be split into other superpositions, do not have to be subjected to the critical-pair-joinability test; it suffices to consider only prime superpositions. As a corollary, this result settles a conjecture of Lankford that unblocked superpositions can be omitted. To prove the result, we introduce new concepts and proof techniques which appear useful for other proofs relating to the Church-Rosser property. This test has been implemented in the completion procedures for ordinary term rewriting systems as well as term rewriting systems with associative-commutative operators. Performance of the completion procedures with this test and without the test are compared on a number of examples in the Rewrite Rule Laboratory (RRL) being developed at General Electric Research and Development Center.