@InProceedings{bahr10rta2,
Title = {Partial Order Infinitary Term Rewriting and Böhm Trees},
Author = {Patrick Bahr},
Booktitle = {Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
Year = {2010},
Address = {Dagstuhl, Germany},
Editor = {Christopher Lynch},
Organization = {Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik},
Pages = {67-84},
Publisher = {Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik},
Series = {Leibniz International Proceedings in Informatics (LIPIcs)},
Volume = {6},
Abstract = {We investigate an alternative model of infinitary term rewriting. Instead of a metric, a partial order on terms is employed to formalise (strong) convergence. We compare this partial order convergence of orthogonal term rewriting systems to the usual metric convergence of the corresponding B{\"o}hm extensions. The B{\"o}hm extension of a term rewriting system contains additional rules to equate so-called root-active terms. The core result we present is that reachability w.r.t. partial order convergence coincides with reachability w.r.t. metric convergence in the B{\"o}hm extension. This result is used to show that, unlike in the metric model, orthogonal systems are infinitarily confluent and infinitarily normalising in the partial order model. Moreover, we obtain, as in the metric model, a compression lemma. A corollary of this lemma is that reachability w.r.t. partial order convergence is a conservative extension of reachability w.r.t. metric convergence.},
Doi = {10.4230/LIPIcs.RTA.2010.67},
ISBN = {978-3-939897-18-7},
ISSN = {1868-8969},
Url = {http://drops.dagstuhl.de/opus/volltexte/2010/2645}
}