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CADE

2010

Springer

2010

Springer

Polynomial interpretations are a useful technique for proving termination of term rewrite systems. In an automated setting, termination tools are concerned with parametric polynomials whose coeﬃcients (i.e., the parameters) are initially unknown and have to be instantiated suitably such that the resulting concrete polynomials satisfy certain conditions. We focus on monotonicity and well-deﬁnedness, the two main conditions that are independent of the respective term rewrite system considered, and provide constraints on the abstract coeﬃcients for linear, quadratic and cubic parametric polynomials such that monotonicity and well-deﬁnedness of the resulting concrete polynomials are guaranteed whenever the constraints are satisﬁed. Our approach subsumes the absolute positiveness approach, which is currently used in many termination tools. In particular, it allows for negative numbers in certain coeﬃcients. We also give an example of a term rewrite system whose termination proof...

Related Content

Added |
13 Jan 2011 |

Updated |
13 Jan 2011 |

Type |
Journal |

Year |
2010 |

Where |
CADE |

Authors |
Friedrich Neurauter, Aart Middeldorp, Harald Zankl |

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