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Generating Polynomial Orderings for Termination Proofs ?

Summary: Generating Polynomial Orderings for
Termination Proofs ?
J¨urgen Giesl
FB Informatik, Technische Hochschule Darmstadt,
Alexanderstr. 10, 64283 Darmstadt, Germany
Email: giesl@inferenzsysteme.informatik.th­darmstadt.de
Abstract. Most systems for the automation of termination proofs using
polynomial orderings are only semi­automatic, i.e. the ``right'' polynomial
ordering has to be given by the user. We show that a variation of Lank­
ford's partial derivative technique leads to an easier and slightly more
powerful method than most other semi­automatic approaches.
Based on this technique we develop a method for the automated synthesis
of a suited polynomial ordering.
1 Introduction
One of the most interesting properties of a term rewriting system (trs) is termi­
nation, cf. [HO80], [DJ90]. A term rewriting system R is terminating for a set of
terms T if there exists no infinite derivation of terms in T . While in general this
problem is undecidable [HL78], several methods for proving termination have
been presented, cf. [Der87a].
This paper is concerned with the automation of termination proofs. Ap­


Source: Ábrahám, Erika - Fachgruppe Informatik, Rheinisch Westfälische Technische Hochschule Aachen (RWTH)


Collections: Computer Technologies and Information Sciences