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Proving Termination by Bounded Increase # Jurgen Giesl, Rene Thiemann, Stephan Swiderski, and Peter SchneiderKamp

Summary: Proving Termination by Bounded Increase #
J˜urgen Giesl, Ren’e Thiemann, Stephan Swiderski, and Peter Schneider­Kamp
LuFG Informatik 2, RWTH Aachen, Germany,
Abstract. Most methods for termination analysis of term rewrite sys­
tems (TRSs) essentially try to find arguments of functions that decrease
in recursive calls. However, they fail if the reason for termination is that
an argument is increased in recursive calls repeatedly until it reaches
a bound. In this paper, we solve that problem and show how to prove
innermost termination of TRSs with bounded increase automatically.
1 Introduction
In programming, one often writes algorithms that terminate because a value is in­
creased until it reaches a bound. Hence, to apply termination techniques of TRSs
in practice, they must be able to deal with those algorithms successfully. But un­
fortunately, all existing methods and tools for automated termination analysis of
TRSs fail on such examples. Therefore, proving termination of TRSs with boun­
ded increase was identified as one of the most urgent and challenging problems
at the annual International Competition of Termination Tools 2006 [16].
Example 1. As an example consider a TRS for subtraction. TRSs of this form
often result from the transformation of conditional TRSs or from functional,


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


Collections: Computer Technologies and Information Sciences