On Dependency Pair Method for Proving Termination of Higher-Order Rewrite Systems

Masahiko SAKAI  Keiichirou KUSAKARI  

IEICE TRANSACTIONS on Information and Systems   Vol.E88-D   No.3   pp.583-593
Publication Date: 2005/03/01
Online ISSN: 
DOI: 10.1093/ietisy/e88-d.3.583
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.