Summary: Modularity of Termination Using
Dependency Pairs ?
Thomas Arts 1 and J¨urgen Giesl 2
1 Computer Science Laboratory, Ericsson Telecom AB, 126 25 Stockholm,
Sweden, E­mail: thomas@cslab.ericsson.se
2 FB Informatik, Darmstadt University of Technology, Alexanderstr. 10,
64283 Darmstadt, Germany, E­mail: giesl@informatik.tu­darmstadt.de
Abstract. The framework of dependency pairs allows automated ter­
mination and innermost termination proofs for many TRSs where such
proofs were not possible before. In this paper we present a refinement of
this framework in order to prove termination in a modular way. Our mod­
ularity results significantly increase the class of term rewriting systems
where termination resp. innermost termination can be proved automat­
ically. Moreover, the modular approach to dependency pairs yields new
modularity criteria which extend previous results in this area. In partic­
ular, existing results for modularity of innermost termination can easily
be obtained as direct consequences of our new criteria.
1 Introduction
Termination is one of the most important properties of a term rewriting system
(TRS). While in general this problem is undecidable [HL78], several methods

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

Collections: Computer Technologies and Information Sciences