Reduction strategies for left-linear term rewriting systems

Yoshihito Toyama

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Citations (Scopus)


Huet and Lévy (1979) showed that needed reduction is a normalizing strategy for orthogonal (i.e., left-linear and non-overlapping) term rewriting systems. In order to obtain a decidable needed reduction strategy, they proposed the notion of strongly sequential approximation. Extending their seminal work, several better decidable approximations of left-linear term rewriting systems, for example, NV approximation, shallow approximation, growing approximation, etc., have been investigated in the literature. In all of these works, orthogonality is required to guarantee approximated decidable needed reductions are actually normalizing strategies. This paper extends these decidable normalizing strategies to left-linear overlapping term rewriting systems. The key idea is the balanced weak Church-Rosser property. We prove that approximated external reduction is a computable normalizing strategy for the class of left-linear term rewriting systems in which every critical pair can be joined with root balanced reductions. This class includes all weakly orthogonal left-normal systems, for example, combinatory logic CL with the overlapping rules pred ·(succ · x) → x and succ · (pred · x) → x, for which leftmost-outermost reduction is a computable normalizing strategy.

Original languageEnglish
Title of host publicationProcesses, Terms and Cycles
Subtitle of host publicationSteps on the Road to Infinity - Essays Dedicated to Jan Willem Klop on the Occasion of His 60th Birthday
PublisherSpringer Verlag
Number of pages26
ISBN (Print)354030911X, 9783540309116
Publication statusPublished - 2005 Jan 1

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3838 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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