Summary: Generating Polynomial Orderings for
Termination Proofs ?
FB Informatik, Technische Hochschule Darmstadt,
Alexanderstr. 10, 64283 Darmstadt, Germany
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.
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