On (Un)Soundness of Unravelings

Authors Karl Gmeiner, Bernhard Gramlich, Felix Schernhammer

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Karl Gmeiner
Bernhard Gramlich
Felix Schernhammer

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Karl Gmeiner, Bernhard Gramlich, and Felix Schernhammer. On (Un)Soundness of Unravelings. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 119-134, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


We revisit (un)soundness of transformations of conditional into unconditional rewrite systems. The focus here is on so-called unravelings, the most simple and natural kind of such transformations, for the class of normal conditional systems without extra variables. By a systematic and thorough study of existing counterexamples and of the potential sources of unsoundness we obtain several new positive and negative results. In particular, we prove the following new results: Confluence, non-erasingness and weak left-linearity (of a given conditional system) each guarantee soundness of the unraveled version w.r.t. the original one. The latter result substantially extends the only known sufficient criterion for soundness, namely left-linearity. Furthermore, by means of counterexamples we refute various other tempting conjectures about sufficient conditions for soundness.
  • Conditional rewriting
  • transformation into unconditional systems
  • unsoundness
  • unraveling


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