{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,13]],"date-time":"2025-09-13T16:33:55Z","timestamp":1757781235573,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,4,29]]},"abstract":"<jats:p>We revisit completion modulo equational theories for left-linear term rewrite systems where unification modulo the theory is avoided and the normal rewrite relation can be used in order to decide validity questions. To that end, we give a new correctness proof for finite runs and establish a simulation result between the two inference systems known from the literature. Given a concrete reduction order, novel canonicity results show that the resulting complete systems are unique up to the representation of their rules' right-hand sides. Furthermore, we show how left-linear AC completion can be simulated by general AC completion. In particular, this result allows us to switch from the former to the latter at any point during a completion process.<\/jats:p>","DOI":"10.46298\/lmcs-21(2:10)2025","type":"journal-article","created":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T11:25:06Z","timestamp":1745925906000},"source":"Crossref","is-referenced-by-count":1,"title":["Left-Linear Completion with AC Axioms"],"prefix":"10.46298","volume":"Volume 21, Issue 2","author":[{"given":"Johannes","family":"Niederhauser","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nao","family":"Hirokawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aart","family":"Middeldorp","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2025,4,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2405.17109v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2405.17109v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T11:25:07Z","timestamp":1745925907000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/13670"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(2:10)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2405.17109v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2405.17109v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2405.17109","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2405.17109","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2025,4,29]]},"article-number":"13670"}}