Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Mechanizing and Improving Dependency Pairs
Journal of Automated Reasoning
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Certification of Termination Proofs Using CeTA
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Termination Of Term Rewriting By Semantic Labelling
Fundamenta Informaticae
Generalized and formalized uncurrying
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Modularity in term rewriting revisited
Theoretical Computer Science
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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We give the first mechanized proof of the fact that for showing termination of a term rewrite system, we may restrict to well-formed terms using just the function symbols actually occurring in the rules of the system. Or equivalently, termination of a term rewrite system is preserved under signature extensions. We did not directly formalize the existing proofs for this well-known result, but developed a new and more elegant proof by reusing facts about dependency pairs. We also investigate signature extensions for termination proofs that use dependency pairs. Here, we were able to develop counterexamples which demonstrate that signature extensions are unsound in general. We further give two conditions where signature extensions are still possible.