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RTA-89 Proceedings of the 3rd international conference on Rewriting Techniques and Applications
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Theory of Computing Systems
Synthesis of max-plus quasi-interpretations
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Information and Computation
Weighted tree automata and weighted logics
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Applicable Algebra in Engineering, Communication and Computing
Matrix Interpretations for Proving Termination of Term Rewriting
Journal of Automated Reasoning
Termination by quasi-periodic interpretations
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Certification of proving termination of term rewriting by matrix interpretations
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Weighted automata for proving termination of string rewriting
Journal of Automata, Languages and Combinatorics
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RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Termination of string rewriting with matrix interpretations
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
A dependency pair framework for innermost complexity analysis of term rewrite systems
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Unifying the Knuth-Bendix, recursive path and polynomial orders
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
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We use weighted tree automata as certificates for termination of term rewriting systems. The weights are taken from the arctic semiring: natural numbers extended with -∞, with the operations "max" and "plus". In order to find and validate these certificates automatically, we restrict their transition functions to be representable by matrix operations in the semiring. The resulting class of weighted tree automata is called path-separated. This extends the matrix method for term rewriting and the arctic matrix method for string rewriting. In combination with the dependency pair method, this allows for some conceptually simple termination proofs in cases where only much more involved proofs were known before. We further generalize to arctic numbers "below zero": integers extended with -∞. This allows to treat some termination problems with symbols that require a predecessor semantics. Correctness of this approach has been formally verified in the Coq proof assistant and the formalization has been contributed to the CoLoR library of certified termination techniques. This allows formal verification of termination proofs using the arctic matrix method in combination with the dependency pair transformation. This contribution brought a substantial performance gain in the certified category of the 2008 edition of the termination competition. The method has been implemented by leading termination provers. We report on experiments with its implementation in one such tool, Matchbox, developed by the second author. We also show that our method can simulate a previous method of quasi-periodic interpretations, if restricted to interpretations of slope one on unary signatures.