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Termination of Constructor Systems ? Thomas Arts 1 and Jurgen Giesl 2

Summary: Termination of Constructor Systems ?
Thomas Arts 1 and J¨urgen Giesl 2
1 Dept. of Computer Science, Utrecht University, P.O. Box 80.089, 3508 TB Utrecht,
The Netherlands, E­mail: thomas@cs.ruu.nl
2 FB Informatik, TH Darmstadt, Alexanderstr. 10, 64283 Darmstadt, Germany,
E­mail: giesl@inferenzsysteme.informatik.th­darmstadt.de
Abstract. We present a method to prove termination of constructor sys­
tems automatically. Our approach takes advantage of the special form of
these rewrite systems because for constructor systems instead of left­ and
right­hand sides of rules it is sufficient to compare so­called dependency
pairs [Art96]. Unfortunately, standard techniques for the generation of
well­founded orderings cannot be directly used for the automation of the
dependency pair approach. To solve this problem we have developed a
transformation technique which enables the application of known synthe­
sis methods for well­founded orderings to prove that dependency pairs
are decreasing. In this way termination of many (also non­simply termi­
nating) constructor systems can be proved fully automatically.
1 Introduction
One of the most interesting properties of a term rewriting system is termina­
tion, cf. e.g. [DJ90]. While in general this problem is undecidable [HL78], sev­


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


Collections: Computer Technologies and Information Sciences