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DOI: 10.4230/OASIcs.WPTE.2014.39
On Proving Soundness of the Computationally Equivalent Transformation for Normal Conditional Term Rewriting Systems by Using Unravelings

Authors: Naoki Nishida, Makishi Yanagisawa, and Karl Gmeiner

Published in: OASIcs, Volume 40, First International Workshop on Rewriting Techniques for Program Transformations and Evaluation (2014)

Abstract
In this paper, we show that the SR transformation, a computationally equivalent transformation proposed by Serbanuta and Rosu, is sound for weakly left-linear normal conditional term rewriting systems (CTRS). Here, soundness for a CTRS means that reduction of the transformed unconditional term rewriting system (TRS) creates no undesired reduction for the CTRS. We first show that every reduction sequence of the transformed TRS starting with a term corresponding to the one considered on the CTRS is simulated by the reduction of the TRS obtained by the simultaneous unraveling. Then, we use the fact that the unraveling is sound for weakly left-linear normal CTRSs.
Cite as

Naoki Nishida, Makishi Yanagisawa, and Karl Gmeiner. On Proving Soundness of the Computationally Equivalent Transformation for Normal Conditional Term Rewriting Systems by Using Unravelings. In First International Workshop on Rewriting Techniques for Program Transformations and Evaluation. Open Access Series in Informatics (OASIcs), Volume 40, pp. 39-50, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{nishida_et_al:OASIcs.WPTE.2014.39,
  author =	{Nishida, Naoki and Yanagisawa, Makishi and Gmeiner, Karl},
  title =	{{On Proving Soundness of the Computationally Equivalent Transformation for Normal Conditional Term Rewriting Systems by Using Unravelings}},
  booktitle =	{First International Workshop on Rewriting Techniques for Program Transformations and Evaluation},
  pages =	{39--50},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-70-5},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{40},
  editor =	{Schmidt-Schau{\ss}, Manfred and Sakai, Masahiko and Sabel, David and Chiba, Yuki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.WPTE.2014.39},
  URN =		{urn:nbn:de:0030-drops-45850},
  doi =		{10.4230/OASIcs.WPTE.2014.39},
  annote =	{Keywords: conditional term rewriting, unraveling, condition elimination}
}
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