Counterexamples to termination for the direct sum of term rewriting systems
Information Processing Letters
Termination of rewriting systems by polynomial interpretations and its implementation
Science of Computer Programming
Journal of Symbolic Computation
Termination of term rewriting: interpretation and type elimination
Journal of Symbolic Computation - Special issue on conditional term rewriting systems
A total AC-compatible ordering based on RPO
RTA-93 Selected papers of the fifth international conference on Rewriting techniques and applications
Simple termination of rewrite systems
NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Type introduction for equational rewriting
Acta Informatica
Proving termination with multiset orderings
Communications of the ACM
Reducing AC-Termination to Termination
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
A New Method for Proving Termination of AC-Rewrite Systems
Proceedings of the Tenth Conference on Foundations of Software Technology and Theoretical Computer Science
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Dummy Elimination in Equational Rewriting
RTA '96 Proceedings of the 7th 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
Termination of Associative-Commutative Rewriting by Dependency Pairs
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Dummy Elimination: Making Termination Easier
FCT '95 Proceedings of the 10th International Symposium on Fundamentals of Computation Theory
Transforming Termination by Self-Labelling
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Termination of a Set of Rules Modulo a Set of Equations
Proceedings of the 7th International Conference on Automated Deduction
Termination Of Term Rewriting By Semantic Labelling
Fundamenta Informaticae
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Semantic labelling is a powerful tool for proving termination of term rewrite systems. The usefulness of the extension to equational term rewriting described in Zantema [24] is however rather limited. In this paper we introduce a stronger version of equational semantical labelling, parameterized by three choices: (1) the order on the underlying algebra (partial order vs. quasi-order), (2) the relation between the algebra and the rewrite system (model vs. quasi-model), and (3) the labelling of the function symbols appearing in the equations (forbidden vs. allowed). We present soundness and completeness results for the various instantiations and analyze the relationships between them. Applications of our equational semantic labelling technique include a short proof of the main result of Ferreira et al. [7]--the correctness of a version of dummy elimination for AC-rewriting which completely removes the AC-axioms-- and an extension of Zantema's distribution elimination technique [23] to the equational setting.