Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
Completion for rewriting modulo a congruence
Theoretical Computer Science - Second Conference on Rewriting Techniques and Applications, Bordeaux, May 1987
Modular proofs for completeness of hierarchical term rewriting systems
Selected papers of the thirteenth conference on Foundations of software technology and theoretical computer science
Term rewriting and all that
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
Advanced topics in term rewriting
Advanced topics in term rewriting
Language Prototyping: An Algebraic Specification Approach: Vol. V
Language Prototyping: An Algebraic Specification Approach: Vol. V
Term Rewriting Systems
ELAN from a rewriting logic point of view
Theoretical Computer Science - Rewriting logic and its applications
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
Dependency Pairs for Equational Rewriting
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Order-Sorted Termination: The Unsorted Way
ALP '96 Proceedings of the 5th International Conference on Algebraic and Logic Programming
Proving Associative-Communicative Termination Using RPO-Compatible Orderings
Selected Papers from Automated Deduction in Classical and Non-Classical Logics
CTRS '94 Proceedings of the 4th International Workshop on Conditional and Typed Rewriting Systems
Proving Termination Using Recursive Path Orders and SAT Solving
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Termination modulo combinations of equational theories
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
All about maude - a high-performance logical framework: how to specify, program and verify systems in rewriting logic
A dependency pair framework for A∨C-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 sufficient completeness checker for linear order-sorted specifications modulo axioms
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
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
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We introduce the notion of well-founded recursive order-sorted equational logic (OS) theories modulo axioms. Such theories define functions by well-founded recursion and are inherently terminating. Moreover, for well-founded recursive theories important properties such as confluence and sufficient completeness are modular for so-called fair extensions. This enables us to incrementally check these properties for hierarchies of such theories that occur naturally in modular rule-based functional programs. Well-founded recursive OS theories modulo axioms contain only commutativity and associativity-commutativity axioms. In order to support arbitrary combinations of associativity, commutativity and identity axioms, we show how to eliminate identity and (under certain conditions) associativity without commutativity) axioms by theory transformations in the last part of the paper.