We investigate a new, Turing-complete class of layered systems, whose linearized lefthand sides of rules can only be overlapped at the root position. Layered systems define a natural notion of rank for terms: the maximal number of redexes along a path from the root to a leaf. Overlappings are allowed in finite or infinite trees. Rules may be non-terminating, non-left-linear, or non-right- linear. Using a novel unification technique, cyclic unification, we show that rank non-increasing layered systems are confluent provided their cyclic critical pairs have cyclic-joinable decreasing diagrams.
@InProceedings{liu_et_al:LIPIcs.CSL.2015.423, author = {Liu, Jiaxiang and Jouannaud, Jean-Pierre and Ogawa, Mizuhito}, title = {{Confluence of Layered Rewrite Systems}}, booktitle = {24th EACSL Annual Conference on Computer Science Logic (CSL 2015)}, pages = {423--440}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-90-3}, ISSN = {1868-8969}, year = {2015}, volume = {41}, editor = {Kreutzer, Stephan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.423}, URN = {urn:nbn:de:0030-drops-54293}, doi = {10.4230/LIPIcs.CSL.2015.423}, annote = {Keywords: Layers, confluence, decreasing diagrams, critical pairs, cyclic unification} }
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