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RTA

2010

Springer

2010

Springer

Polynomial interpretations are a useful technique for proving termination of term rewrite systems. They come in various ﬂavors: polynomial interpretations with real, rational and integer coeﬃcients. In 2006, Lucas proved that there are rewrite systems that can be shown polynomially terminating by polynomial interpretations with real (algebraic) coeﬃcients, but cannot be shown polynomially terminating using polynomials with rational coeﬃcients only. He also proved a similar theorem with respect to the use of rational coeﬃcients versus integer coeﬃcients. In this paper we show that polynomial interpretations with real or rational coeﬃcients do not subsume polynomial interpretations with integer coeﬃcients, contrary to what is commonly believed. We further show that polynomial interpretations with real coeﬃcients subsume polynomial interpretations with rational coeﬃcients.

Related Content

Added |
30 Jan 2011 |

Updated |
30 Jan 2011 |

Type |
Journal |

Year |
2010 |

Where |
RTA |

Authors |
Friedrich Neurauter, Aart Middeldorp |

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