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Eliminating Dummy Elimination ? Jurgen Giesl 1 and Aart Middeldorp 2

Summary: Eliminating Dummy Elimination ?
Jurgen Giesl 1 and Aart Middeldorp 2
1 Computer Science Department
University of New Mexico, Albuquerque, NM 87131, USA
2 Institute of Information Sciences and Electronics
University of Tsukuba, Tsukuba 305-8573, Japan
Abstract. This paper is concerned with methods that automatically
prove termination of term rewrite systems. The aim of dummy elimina-
tion, a method to prove termination introduced by Ferreira and Zantema,
is to transform a given rewrite system into a rewrite system whose termi-
nation is easier to prove. We show that dummy elimination is subsumed
by the more recent dependency pair method of Arts and Giesl. More pre-
cisely, if dummy elimination succeeds in transforming a rewrite system
into a so-called simply terminating rewrite system then termination of
the given rewrite system can be directly proved by the dependency pair
technique. Even stronger, using dummy elimination as a preprocessing
step to the dependency pair technique does not have any advantages
either. We show that to a large extent these results also hold for the


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


Collections: Computer Technologies and Information Sciences