Termination of Generalized Term Rewriting Systems

Author Salvador Lucas

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Salvador Lucas
  • DSIC & VRAIN, Universitat Politècnica de València, Spain, Spain


I thank the reviewers for their useful comments leading to several improvements in the paper. I also thank Raúl Gutiérrez for his comments.

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Salvador Lucas. Termination of Generalized Term Rewriting Systems. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


We investigate termination of Generalized Term Rewriting Systems (GTRS), which extend Conditional Term Rewriting Systems by considering replacement restrictions on selected arguments of function symbols, as in Context-Sensitive Rewriting, and conditional rewriting rules whose conditional part may include not only a mix of the usual (reachability, joinability,...) conditions, but also atoms defined by a set of definite Horn clauses. GTRS can be used to prove confluence and termination of Generalized Rewrite Theories and Maude programs. We have characterized confluence of terminating GTRS as the joinability of a finite set of conditional pairs. Since termination of GTRS is underexplored to date, this paper introduces a Dependency Pair Framework which is well-suited to automatically (dis)prove termination of GTRS.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automated reasoning
  • Theory of computation → Logic and verification
  • Theory of computation → Equational logic and rewriting
  • Program Analysis
  • Reduction-Based Systems
  • Termination


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  1. Beatriz Alarcón, Raúl Gutiérrez, and Salvador Lucas. Context-sensitive dependency pairs. Inf. Comput., 208(8):922-968, 2010. URL: https://doi.org/10.1016/j.ic.2010.03.003.
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