Decidability for left-linear growing term rewriting systems

Takashi Nagaya, Yoshihito Toyama

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


A term rewriting system is called growing if each variable occurring on both the left-hand side and the right-hand side of a rewrite rule occurs at depth zero or one in the left-hand side. Jacquemard showed that the reachability and the sequentiality of linear (i.e., left-right-linear) growing term rewriting systems are decidable. In this paper we show that Jacquemard's result can be extended to left-linear growing rewriting systems that may have right-nonlinear rewrite rules. This implies that the reachability and the joinability of some class of right-linear term rewriting systems are decidable, which improves the results for right-ground term rewriting systems by Oyamaguchi. Our result extends the class of left-linear term rewriting systems having a decidable call-by-need normalizing strategy. Moreover, we prove that the termination property is decidable for almost orthogonal growing term rewriting systems.

Original languageEnglish
Pages (from-to)499-514
Number of pages16
JournalInformation and Computation
Issue number2
Publication statusPublished - 2002 Nov 1
Externally publishedYes


  • Growing term rewriting system
  • Joinability
  • Reachability
  • Sequentiality

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics


Dive into the research topics of 'Decidability for left-linear growing term rewriting systems'. Together they form a unique fingerprint.

Cite this