Higher-order rewrite systems and their confluence
Theoretical Computer Science - Special issue: rewriting systems and applications
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Modular termination proofs for rewriting using dependency pairs
Journal of Symbolic Computation
Confluence and Termination of Simply Typed Term Rewriting Systems
RTA '01 Proceedings of the 12th 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
On Dependency Pair Method for Proving Termination of Higher-Order Rewrite Systems
IEICE - Transactions on Information and Systems
Termination of simply typed term rewriting by translation and labelling
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Tyrolean termination tool: Techniques and features
Information and Computation
Proceedings of the 10th international ACM SIGPLAN conference on Principles and practice of declarative programming
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Argument filterings and usable rules for simply typed dependency pairs
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Harnessing first order termination provers using higher order dependency pairs
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Proving and disproving termination of higher-order functions
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
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Simply typed term rewriting proposed by Yamada (RTA, 2001) is a framework of higher-order term rewriting without bound variables. In this paper, the dependency pair method of first-order term rewriting introduced by Arts and Giesl (TCS, 2000) is extended in order to show termination of simply typed term rewriting systems. Basic concepts such as dependency pairs and estimated dependency graph in the simply typed term rewriting framework are clarified. The subterm criterion introduced by Hirokawa and Middeldorp (RTA, 2004) is successfully extended to the case where terms of function type are allowed. Finally, an experimental result for a collection of simply typed term rewriting systems is presented. Our method is compared with the direct application of the first-order dependency pair method to a first-order encoding of simply typed term rewriting systems.