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.
@InProceedings{kim_et_al:LIPIcs.FSCD.2021.19, author = {Kim, Dohan and Lynch, Christopher}, title = {{An RPO-Based Ordering Modulo Permutation Equations and Its Applications to Rewrite Systems}}, booktitle = {6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)}, pages = {19:1--19:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-191-7}, ISSN = {1868-8969}, year = {2021}, volume = {195}, editor = {Kobayashi, Naoki}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.19}, URN = {urn:nbn:de:0030-drops-142572}, doi = {10.4230/LIPIcs.FSCD.2021.19}, annote = {Keywords: Recursive Path Ordering, Permutation Equation, Permutation Group, Rewrite System, Completion, Ground Completion} }
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