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On Dependency Pair Method for Proving Termination of Higher-Order Rewrite Systems
Masahiko SAKAI Keiichirou KUSAKARI
IEICE TRANSACTIONS on Information and Systems
Publication Date: 2005/03/01
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Computation and Computational Models
termination, dependency pair, higher-order rewrite system, dependency forest,
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This paper explores how to extend the dependency pair technique for proving termination of higher-order rewrite systems. In the first order case, the termination of term rewriting systems are proved by showing the non-existence of an infinite R-chain of the dependency pairs. However, the termination and the non-existence of an infinite R-chain do not coincide in the higher-order case. We introduce a new notion of dependency forest that characterize infinite reductions and infinite R-chains, and show that the termination property of higher-order rewrite systems R can be checked by showing the non-existence of an infinite R-chain, if R is strongly linear or non-nested.