Handbook of formal languages, vol. 3
Term rewriting and all that
Termination of Linear Rewriting Systems (Preliminary Version)
Proceedings of the 8th Colloquium on Automata, Languages and Programming
Decidable Approximations of Sets of Descendants and Sets of Normal Forms
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Automated Termination Proofs with Measure Functions
KI '95 Proceedings of the 19th Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Match-Bounded String Rewriting Systems
Applicable Algebra in Engineering, Communication and Computing
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
On tree automata that certify termination of left-linear term rewriting systems
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Finding finite automata that certify termination of string rewriting
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
Tyrolean termination tool: Techniques and features
Information and Computation
On tree automata that certify termination of left-linear term rewriting systems
Information and Computation
Bottom-up rewriting is inverse recognizability preserving
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Weighted automata for proving termination of string rewriting
Journal of Automata, Languages and Combinatorics
On tree automata that certify termination of left-linear term rewriting systems
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
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We present a new method for proving termination of term rewriting systems automatically. It is a generalization of the match bound method for string rewriting. To prove that a term rewriting system terminates on a given regular language of terms, we first construct an enriched system over a new signature that simulates the original derivations. The enriched system is an infinite system over an infinite signature, but it is locally terminating: every restriction of the enriched system to a finite signature is terminating. We then construct iteratively a finite tree automaton that accepts the enriched given regular language and is closed under rewriting modulo the enriched system. If this procedure stops, then the enriched system is compact: every enriched derivation involves only a finite signature. Therefore, the original system terminates. We present three methods to construct the enrichment: top heights, roof heights, and match heights. Top and roof heights work for left-linear systems, while match heights give a powerful method for linear systems. For linear systems, the method is strengthened further by a forward closure construction. Using these methods, we give examples for automated termination proofs that cannot be obtained by standard methods.