### Abstract

A bridge is presented between term-rewriting theory in computer science and proof theory in logic. It is shown that proof-theoretic tools are very useful for analyzing two basic attributes of term rewriting systems, the termination property and the Church-Rosser property. A counterexample is given to show that Knuth's critical pair lemma does not hold for conditional rewrite systems. Two restrictions on conditional systems under which the critical pair lemma holds are presented. One is considered a generalization of Bergstra-Klop's former result; the other is concerned with a generalization of Kaplan's and Jouannaud-Waldmann's systems.

Original language | English |
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Title of host publication | Proc Third Annu Symp on Logic in Comput Sci |

Publisher | Publ by IEEE |

Pages | 104-111 |

Number of pages | 8 |

ISBN (Print) | 0818608536 |

Publication status | Published - 1988 Dec 1 |

Externally published | Yes |

### Publication series

Name | Proc Third Annu Symp on Logic in Comput Sci |
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### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

*Proc Third Annu Symp on Logic in Comput Sci*(pp. 104-111). (Proc Third Annu Symp on Logic in Comput Sci). Publ by IEEE.