some image logo

HOME

SEARCH

CURRENT ISSUE

REGULAR ISSUES

   Volume 1 (2005)

   Volume 2 (2006)

   Volume 3 (2007)

   Volume 4 (2008)

   Volume 5 (2009)

   Volume 6 (2010)

   Volume 7 (2011)

   Volume 8 (2012)

      Issue 1

      Issue 2

      Issue 3

      Issue 4

   Volume 9 (2013)

   Volume 10 (2014)

   Volume 11 (2015)

   Volume 12 (2016)

   Volume 13 (2017)

SPECIAL ISSUES

SURVEY ARTICLES

AUTHORS

ABOUT

SERVICE

LOGIN

FAQ

SUPPORT

CONTACT

VOLUME 8, ISSUE 1, PAPER 31


A Reduction-Preserving Completion for Proving Confluence of Non-Terminating Term Rewriting Systems

©Takahito Aoto, Tohoku University
©Yoshihito Toyama, Tohoku University

Abstract
We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critical pairs and it also (partially) works even if the system is not terminating modulo E. We first present confluence criteria for term rewriting systems whose rewrite rules can be partitioned into a terminating part and a possibly non-terminating part. We then give a reduction-preserving completion procedure so that the applicability of the criteria is enhanced. In contrast to the well-known Knuth-Bendix completion procedure which preserves the equivalence relation of the system, our completion procedure preserves the reduction relation of the system, by which confluence of the original system is inferred from that of the completed system.

Publication date: March 28, 2012

Full Text: PDF | PostScript
DOI: 10.2168/LMCS-8(1:31)2012

Hit Counts: 5984

Creative Commons