Eliminating Dummy Elimination ?

Eliminating Dummy Elimination

This paper is concerned with methods that automatically prove termination of term rewrite systems. The aim of dummy elimination, a method to prove termination introduced by Ferreira and Zantema, is to transform a given rewrite system into a rewrite system whose termination is easier to prove. We show that dummy elimination is subsumed by the more recent dependency pair method of Arts and Giesl....

Argument Filtering Transformation

To simplify the task of proving termination of term rewriting systems, several elimination methods, such as the dummy elimination, the distribution elimination, the general dummy elimination and the improved general dummy elimination, have been proposed. In this paper, we show that the argument ltering method combining with the dependency pair technique is essential in all the above elimination...

Termination , AC - Termination and Dependency Pairs of Term Rewriting Systems

Recently, Arts and Giesl introduced the notion of dependency pairs, which gives effective methods for proving termination of term rewriting systems (TRSs). In this thesis, we extend the notion of dependency pairs to AC-TRSs, and introduce new methods for effectively proving AC-termination. Since it is impossible to directly apply the notion of dependency pairs to AC-TRSs, we introduce the head ...

Dummy Elimination: Making Termination Easier

Termination Transformation by Tree Lifting Ordering

An extension of a modular termination result for term rewriting systems (TRSs, for short) by A. Middeldorp (1989) is presented. We intended to obtain this by adapting the dummy elimination transformation by M. C. F. Ferreira and H. Zantema (1995) under the presence of a non-collapsing non-duplicating terminating TRS whose function symbols are all to be eliminated. We propose a tree lifting orde...