Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
Termination of rewriting systems by polynomial interpretations and its implementation
Science of Computer Programming
Completion for rewriting modulo a congruence
Theoretical Computer Science - Second Conference on Rewriting Techniques and Applications, Bordeaux, May 1987
Combining matching algorithms: The regular case
Journal of Symbolic Computation
Termination and completion modulo associativity, commutativity and identity
Theoretical Computer Science - Selected papers on theoretical issues of design and implementation of symbolic computation systems
A total AC-compatible ordering based on RPO
RTA-93 Selected papers of the fifth international conference on Rewriting techniques and applications
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
Advanced topics in term rewriting
Advanced topics in term rewriting
Equational rules for rewriting logic
Theoretical Computer Science - Rewriting logic and its applications
Operational Semantics of OBJ-3 (Extended Abstract)
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Combination of Matching Algorithms
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Dummy Elimination in Equational Rewriting
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Termination of Associative-Commutative Rewriting by Dependency Pairs
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Proving operational termination of membership equational programs
Higher-Order and Symbolic Computation
Variant Narrowing and Equational Unification
Electronic Notes in Theoretical Computer Science (ENTCS)
Operational Termination of Membership Equational Programs: the Order-Sorted Way
Electronic Notes in Theoretical Computer Science (ENTCS)
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
The finite variant property: how to get rid of some algebraic properties
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
A dependency pair framework for A∨C-termination
WRLA'10 Proceedings of the 8th international conference on Rewriting logic and its applications
Folding variant narrowing and optimal variant termination
WRLA'10 Proceedings of the 8th international conference on Rewriting logic and its applications
A Church-Rosser checker tool for conditional order-sorted equational Maude specifications
WRLA'10 Proceedings of the 8th international conference on Rewriting logic and its applications
A Maude coherence checker tool for conditional order-sorted rewrite theories
WRLA'10 Proceedings of the 8th international conference on Rewriting logic and its applications
Incremental checking of well-founded recursive specifications modulo axioms
Proceedings of the 13th international ACM SIGPLAN symposium on Principles and practices of declarative programming
Towards a Maude formal environment
Formal modeling
Order-Sorted equality enrichments modulo axioms
WRLA'12 Proceedings of the 9th international conference on Rewriting Logic and Its Applications
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Rewriting with rules R modulo axioms E is a widely used technique in both rule-based programming languages and in automated deduction. Termination methods for rewriting systems modulo specific axioms E (e.g., associativity-commutativity) are known. However, much less seems to be known about termination methods that can be modular in the set E of axioms. In fact, current termination tools and proof methods cannot be applied to commonly occurring combinations of axioms that fall outside their scope. This work proposes a modular termination proof method based on semantics- and termination-preserving transformations that can reduce the proof of termination of rules R modulo E to an equivalent proof of termination of the transformed rules modulo a typically much simpler set B of axioms. Our method is based on the notion of variants of a term recently proposed by Comon and Delaune. We illustrate its practical usefulness by considering the very common case in which E is an arbitrary combination of associativity, commutativity, left- and right-identity axioms for various function symbols.