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Proving Innermost Normalisation Automatically ? Thomas Arts 1 and Jurgen Giesl 2

Summary: Proving Innermost Normalisation Automatically ?
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 technique to prove innermost normalisation
of term rewriting systems (TRSs) automatically. In contrast to previous
methods, our technique is able to prove innermost normalisation of TRSs
that are not terminating.
Our technique can also be used for termination proofs of all TRSs where
innermost normalisation implies termination, such as non­overlapping
TRSs or locally confluent overlay systems. In this way, termination of
many (also non­simply terminating) TRSs can be verified automatically.
1 Introduction
Innermost rewriting, i.e. rewriting where only innermost redeces are contracted,
can be used to model call­by­value computation semantics. For that reason,
there has been an increasing interest in innermost normalisation (also called
innermost termination), i.e. in proving that the length of every innermost reduc­
tion is finite. Techniques for proving innermost normalisation can for example


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


Collections: Computer Technologies and Information Sciences