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Abstract Relations Between Restricted Termination And Confluence Properties Of Rewrite Systems

Author:

Bernhard GramlichAuthors Info & Claims

Fundamenta Informaticae, Volume 24, Issue 1-2

Pages 3 - 23

Published: 01 April 1995 Publication History

Abstract

We investigate restricted termination and confluence properties of term rewriting systems, in particular weak termination, weak innermost termination, (strong) innermost termination, (strong) termination, and their interrelations. New criteria are provided which are sufficient for the equivalence of these properties. These criteria provide interesting possibilities to infer completeness, i.e. termination plus confluence, from restricted termination and confluence properties. Our main result states that any (strongly) innermost terminating, locally confluent overlay system is terminating, and hence confluent and complete. Using these basic results we are also able to prove some new results about modular termination of rewriting. In particular, we show that termination is modular for some classes of innermost terminating and locally confluent term rewriting systems, namely for non-overlapping and even for overlay systems. As an easy consequence this latter result also entails a simplified proof of the fact that completeness is a decomposable property of constructor systems. Similarly, a combined overlay system with shared constructors is complete if and only if its component sytems are complete overlay systems. Interestingly, these modularity results are obtained by means of a proof technique which itself constitutes a modular approach.

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Cited By

Ishizuki SOyamaguchi MSakai M(2019)Conditions for confluence of innermost terminating term rewriting systemsApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-018-0377-830:4(349-360)Online publication date: 2-Aug-2019
https://dl.acm.org/doi/10.1007/s00200-018-0377-8
Giesl JThiemann RSchneider-Kamp PFalke S(2018)Mechanizing and Improving Dependency PairsJournal of Automated Reasoning10.1007/s10817-006-9057-737:3(155-203)Online publication date: 28-Dec-2018
https://dl.acm.org/doi/10.1007/s10817-006-9057-7
Avanzini MDal Lago UMoser G(2015)Analysing the complexity of functional programs: higher-order meets first-orderACM SIGPLAN Notices10.1145/2858949.278475350:9(152-164)Online publication date: 29-Aug-2015
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Abstract Relations Between Restricted Termination And Confluence Properties Of Rewrite Systems
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cover image Fundamenta Informaticae

Fundamenta Informaticae Volume 24, Issue 1-2

April 1995

201 pages

ISSN:0169-2968

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IOS Press

Netherlands

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Published: 01 April 1995

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Cited By

Ishizuki SOyamaguchi MSakai M(2019)Conditions for confluence of innermost terminating term rewriting systemsApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-018-0377-830:4(349-360)Online publication date: 2-Aug-2019
https://dl.acm.org/doi/10.1007/s00200-018-0377-8
Giesl JThiemann RSchneider-Kamp PFalke S(2018)Mechanizing and Improving Dependency PairsJournal of Automated Reasoning10.1007/s10817-006-9057-737:3(155-203)Online publication date: 28-Dec-2018
https://dl.acm.org/doi/10.1007/s10817-006-9057-7
Avanzini MDal Lago UMoser G(2015)Analysing the complexity of functional programs: higher-order meets first-orderACM SIGPLAN Notices10.1145/2858949.278475350:9(152-164)Online publication date: 29-Aug-2015
https://dl.acm.org/doi/10.1145/2858949.2784753
Avanzini MDal Lago UMoser GFisher KReppy J(2015)Analysing the complexity of functional programs: higher-order meets first-orderProceedings of the 20th ACM SIGPLAN International Conference on Functional Programming10.1145/2784731.2784753(152-164)Online publication date: 29-Aug-2015
https://dl.acm.org/doi/10.1145/2784731.2784753
Winkler SThiemann R(2015)Formalizing Soundness and Completeness of UnravelingsProceedings of the 10th International Symposium on Frontiers of Combining Systems - Volume 932210.1007/978-3-319-24246-0_15(239-255)Online publication date: 21-Sep-2015
https://dl.acm.org/doi/10.1007/978-3-319-24246-0_15
Fuhs CKop C(2011)Harnessing first order termination provers using higher order dependency pairsProceedings of the 8th international conference on Frontiers of combining systems10.5555/2050784.2050797(147-162)Online publication date: 5-Oct-2011
https://dl.acm.org/doi/10.5555/2050784.2050797
Gnaedig IKirchner H(2009)Termination of rewriting under strategiesACM Transactions on Computational Logic10.1145/1462179.146218210:2(1-52)Online publication date: 2-Mar-2009
https://dl.acm.org/doi/10.1145/1462179.1462182
Gnaedig ILeuschel MPodelski A(2007)Induction for positive almost sure terminationProceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming10.1145/1273920.1273943(167-178)Online publication date: 14-Jul-2007
https://dl.acm.org/doi/10.1145/1273920.1273943
Alarcón BLucas S(2007)Termination of Innermost Context-Sensitive Rewriting Using Dependency PairsProceedings of the 6th international symposium on Frontiers of Combining Systems10.1007/978-3-540-74621-8_5(73-87)Online publication date: 10-Sep-2007
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van de Pol JZantema H(2005)Generalized innermost rewritingProceedings of the 16th international conference on Term Rewriting and Applications10.1007/978-3-540-32033-3_2(2-16)Online publication date: 19-Apr-2005
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