Termination orderings for associative-commutative rewriting systems
Journal of Symbolic Computation
Termination of rewriting systems by polynomial interpretations and its implementation
Science of Computer Programming
A total AC-compatible ordering based on RPO
RTA-93 Selected papers of the fifth international conference on Rewriting techniques and applications
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Argument Filtering Transformation
PPDP '99 Proceedings of the International Conference PPDP'99 on Principles and Practice of Declarative Programming
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
Rewrite Systems for Natural, Integral, and Rational Arithmetic
RTA '97 Proceedings of the 8th 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
Complete Monotonic Semantic Path Orderings
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Orderings and constraints: theory and practice of proving termination
Rewriting Computation and Proof
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Polynomial interpretations and RPO-like orderings allow one to prove termination of Associative and Commutative (AC-)rewriting by only checking the rules of the given rewrite system. However, these methods have important limitations as termination proving tools. To overcome these limitations, more powerful methods like the dependency pair method have been extended to the AC-case. Unfortunately, in order to ensure AC-termination, the so-called extended rules, which, in general are hard to prove must be added to the rewrite system. In this paper we present a fully monotonic AC-compatible semantic path ordering. This monotonic AC-ordering defines a new automatable termination proving method for AC-rewritingwhic h does not need to consider extended rules. As a hint of the power of this method, we can easily prove several non-trivial examples appearing in the literature, including one that, to our knowledge, can be handled by no other automatic method.