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An RPO-Based Ordering Modulo Permutation Equations and Its Applications to Rewrite Systems

Authors Dohan Kim, Christopher Lynch

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  • 17 pages

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Dohan Kim
  • Clarkson University, Potsdam, NY, USA
Christopher Lynch
  • Clarkson University, Potsdam, NY, USA

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Dohan Kim and Christopher Lynch. An RPO-Based Ordering Modulo Permutation Equations and Its Applications to Rewrite Systems. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 19:1-19:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


Rewriting modulo equations has been researched for several decades but due to the lack of suitable orderings, there are some limitations to rewriting modulo permutation equations. Given a finite set of permutation equations E, we present a new RPO-based ordering modulo E using (permutation) group actions and their associated orbits. It is an E-compatible reduction ordering on terms with the subterm property and is E-total on ground terms. We also present a completion and ground completion method for rewriting modulo a finite set of permutation equations E using our ordering modulo E. We show that our ground completion modulo E always admits a finite ground convergent (modulo E) rewrite system, which allows us to obtain the decidability of the word problem of ground theories modulo E.

Subject Classification

ACM Subject Classification
  • Theory of computation → Equational logic and rewriting
  • Recursive Path Ordering
  • Permutation Equation
  • Permutation Group
  • Rewrite System
  • Completion
  • Ground Completion


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