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Modes of Convergence for Term Graph Rewriting Bahr, Patrick term graphs partial order metric infinitary rewriting graph rewriting Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour is impaired by the lack of an appropriate counterpart of infinitary rewriting on the side of term graphs. We aim to fill this gap by devising two modes of convergence based on a partial order resp. a metric on term graphs. The thus obtained structures generalise corresponding modes of convergence that are usually studied in infinitary term rewriting. We argue that this yields a common framework in which both term rewriting and term graph rewriting can be studied. In order to substantiate our claim, we compare convergence on term graphs and on terms. In particular, we show that the resulting infinitary calculi of term graph rewriting exhibit the same correspondence as we know it from term rewriting: Convergence via the partial order is a conservative extension of the metric convergence. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Patrick Bahr 2011 Is Part Of LIPIcs, Volume 10, 22nd International Conference on Rewriting Techniques and Applications (RTA'11) (2011) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.RTA.2011.139 urn:nbn:de:0030-drops-31131 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2011.139 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode