### Abstract

A term rewriting system is called growing if each variable occurring 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-non-linear 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 rightground 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 language | English |
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Title of host publication | Rewriting Techniques and Applications - 10th International Conference, RTA 1999, Proceedings |

Editors | Paliath Narendran, Michael Rusinowitch |

Publisher | Springer Verlag |

Pages | 256-270 |

Number of pages | 15 |

ISBN (Print) | 3540662014, 9783540662013 |

DOIs | |

Publication status | Published - 1999 Jan 1 |

Event | 10th International Conference on Rewriting Techniques and Applications, RTA 1999 - Trento, Italy Duration: 1999 Jul 2 → 1999 Jul 4 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1631 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 10th International Conference on Rewriting Techniques and Applications, RTA 1999 |
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Country | Italy |

City | Trento |

Period | 99/7/2 → 99/7/4 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Rewriting Techniques and Applications - 10th International Conference, RTA 1999, Proceedings*(pp. 256-270). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1631). Springer Verlag. https://doi.org/10.1007/3-540-48685-2_22