Termination orderings for associative-commutative rewriting systems
Journal of Symbolic Computation
Proving termination of associative commutative rewriting systems by rewriting
Proc. of the 8th international conference on Automated deduction
Termination of rewriting systems by polynomial interpretations and its implementation
Science of Computer Programming
Journal of Symbolic Computation
Improving associative path orderings
CADE-10 Proceedings of the tenth international conference on Automated deduction
Maximal Extensions os Simplification Orderings
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
Any Gound Associative-Commutative Theory Has a Finite Canonical System
RTA '91 Proceedings of the 4th International Conference on Rewriting Techniques and Applications
A Precedence-Based Total AC-Compatible Ordering
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
Extension of the Associative Path Ordering to a Chain of Associative Commutative Symbols
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
A Total, Ground path Ordering for Proving Termination of AC-Rewrite Systems
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Dependency Pairs for Rewriting with Non-free Constructors
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Incremental checking of well-founded recursive specifications modulo axioms
Proceedings of the 13th international ACM SIGPLAN symposium on Principles and practices of declarative programming
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Developing path orderings for associative-commutative (AC) rewrite systems has been quite a challenge at least for a decade. Compatibility with the recursive path ordering (RPO) schemes is desirable, and this property helps in orienting the commonly encountered distributivity axiom as desired. For applications in theorem proving and constraint solving, a total ordering on ground terms involving AC operators is often required. It is shown how the main solutions proposed so far ([7],[13]) with the desired properties can be viewed as arising from a common framework. A general scheme that works for non-ground (general) terms also is proposed. The proposed definition allows flexibility (using different abstractions) in the way the candidates of a term with respect to an associative-commutative function symbol are compared, thus leading to at least two distinct orderings on terms (from the same precedence relation on function symbols)