A Proof Method for Local Sufficient Completeness of Term Rewriting Systems

A term rewriting system (TRS) is said to be sufficiently complete when each function yields some value for any input. In this paper, we present a proof method for local sufficient completeness of TRSs, which is a generalised notion of sufficient completeness and is useful for proving inductive theor...

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Bibliographic Details
Published inTheoretical Aspects of Computing - ICTAC 2021 Vol. 12819; pp. 386 - 404
Main Authors Shiraishi, Tomoki, Kikuchi, Kentaro, Aoto, Takahito
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2021
Springer International Publishing
SeriesLecture Notes in Computer Science
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Summary:A term rewriting system (TRS) is said to be sufficiently complete when each function yields some value for any input. In this paper, we present a proof method for local sufficient completeness of TRSs, which is a generalised notion of sufficient completeness and is useful for proving inductive theorems of non-terminating TRSs. The proof method is based on a sufficient condition for local sufficient completeness of TRSs that consist of functions on natural numbers and (possibly infinite) lists of natural numbers. We also make a comparison between the proof abilities of the methods by the sufficient condition and by a derivation system introduced in previous work.
ISBN:3030853144
9783030853143
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-030-85315-0_22