Summary: Automatically Proving Termination Where
Simplification Orderings Fail ?
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. To prove termination of term rewriting systems (TRSs), sev­
eral methods have been developed to synthesize suitable well­founded or­
derings automatically. However, virtually all orderings that are amenable
to automation are so­called simplification orderings. Unfortunately, there
exist numerous interesting and relevant TRSs that cannot be oriented by
orderings of this restricted class and therefore their termination cannot
be proved automatically with the existing techniques.
In this paper we present a new approach which allows to apply the stan­
dard techniques for automated termination proofs to those TRSs where
these techniques failed up to now. For that purpose we have developed
a procedure which, given a TRS, generates a set of inequalities (con­
straints) automatically. If there exists a well­founded ordering satisfying
these constraints, then the TRS is terminating. It turns out that for many

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

Collections: Computer Technologies and Information Sciences