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Polygraphs for termination of left-linear term rewriting systems

Yves Guiraud 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We present a methodology for proving termination of left-linear term rewriting systems (TRSs) by using Albert Burroni's polygraphs, a kind of rewriting systems on algebraic circuits. We translate the considered TRS into a polygraph of minimal size whose termination is proven with a polygraphic interpretation, then we get back the property on the TRS. We recall Yves Lafont's general translation of TRSs into polygraphs and known links between their termination properties. We give several conditions on the original TRS, including being a first-order functional program, that ensure that we can reduce the size of the polygraphic translation. We also prove sufficient conditions on the polygraphic interpretations of a minimal translation to imply termination of the original TRS. Examples are given to compare this method with usual polynomial interpretations.
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https://hal.inria.fr/inria-00129392
Contributor : Yves Guiraud <>
Submitted on : Wednesday, February 7, 2007 - 11:02:25 AM
Last modification on : Friday, February 26, 2021 - 3:28:06 PM
Long-term archiving on: : Friday, September 21, 2012 - 11:12:43 AM

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  • HAL Id : inria-00129392, version 1

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Yves Guiraud. Polygraphs for termination of left-linear term rewriting systems. 2007. ⟨inria-00129392⟩

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