Simple termination revisited
 Aart Middeldorp,
 Hans Zantema
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Abstract
In this paper we investigate the concept of simple termination. A term rewriting system is called simply terminating if its termination can be proved by means of a simplification order. The basic ingredient of a simplification order is the subterm property, but in the literature two different definitions are given: one based on (strict) partial orders and another one based on preorders (or quasiorders). In the first part of the paper we argue that there is no reason to choose the second one, while the first one has certain advantages.
Simplification orders are known to be wellfounded orders on terms over a finite signature. This important result no longer holds if we consider infinite signatures. Nevertheless, wellknown simplification orders like the recursive path order are also wellfounded on terms over infinite signatures, provided the underlying precedence is wellfounded. We propose a new definition of simplification order, which coincides with the old one (based on partial orders) in case of finite signatures, but which is also wellfounded over infinite signatures and covers orders like the recursive path order.
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 Title
 Simple termination revisited
 Book Title
 Automated Deduction — CADE12
 Book Subtitle
 12th International Conference on Automated Deduction Nancy, France, June 26 – July 1, 1994 Proceedings
 Pages
 pp 451465
 Copyright
 1994
 DOI
 10.1007/3540581561_33
 Print ISBN
 9783540581567
 Online ISBN
 9783540484677
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 814
 Series Subtitle
 Lecture Notes in Artificial Intelligence (LNAI)
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Aart Middeldorp ^{(1)}
 Hans Zantema ^{(2)}
 Author Affiliations

 1. Institute of Information Sciences and Electronics, University of Tsukuba, 305, Tsukuba, Japan
 2. Department of Computer Science, Utrecht University, P.O. Box 80.089, 3508, TB Utrecht, The Netherlands
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