Refutational theorem proving using term-rewriting systems
Artificial Intelligence
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
Proving termination with multiset orderings
Communications of the ACM
Abstract data types and software validation
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
Termination of a Set of Rules Modulo a Set of Equations
Proceedings of the 7th 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
Decomposition ordering at a tool to prove the termination of rewriting systems
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 1
Associative-commutative rewriting
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
History and basic features of the critical-pair/completion procedure
Journal of Symbolic Computation
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Proving Associative-Communicative Termination Using RPO-Compatible Orderings
Selected Papers from Automated Deduction in Classical and Non-Classical Logics
Elimination Transformations for Associative---Commutative Rewriting Systems
Journal of Automated Reasoning
Equational reasoning using AC constraints
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Monotonic AC-compatible semantic path orderings
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Simplification Orderings: History Of Results
Fundamenta Informaticae
A term rewriting system for the calculus of moving surfaces
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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In this paper we describe a new class of orderings-associative path orderings-for proving termination of associative-commutative term rewriting systems .These orderings are based on the concept of simplification orderings and extend the well-known recursive path orderings to E - congruence classes, where E is an equational theory consisting of associativity and commutativity axioms. Associative path orderings are applicable to term rewriting systems for which a precedence ordering on the set of operator symbols can be defined that satisfies a certain condition,the associative path condition. The precedence ordering can often be derived from the structure of the reduction rules. We include termination proofs for various term rewriting systems (for rings,boolean algebra,etc.) and, in addition, point out ways to handle situations where the associative path condition is too restrictive.