Summary: To appear in
Applicable Algebra in Engineering, Communication and Comp.
The Size­Change Principle and Dependency
Pairs for Termination of Term Rewriting
Ren’e Thiemann and J˜urgen Giesl
LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074 Aachen, Germany
E­mail: {thiemann|giesl}@informatik.rwth­aachen.de
The date of receipt and acceptance will be inserted by the editor
Abstract In [24], a new size­change principle was proposed to verify ter­
mination of functional programs automatically. We extend this principle
in order to prove termination and innermost termination of arbitrary term
rewrite systems (TRSs). Moreover, we compare this approach with existing
techniques for termination analysis of TRSs (such as recursive path orders or
dependency pairs). It turns out that the size­change principle on its own fails
for many examples that can be handled by standard techniques for rewrit­
ing, but there are also TRSs where it succeeds whereas existing rewriting
techniques fail. Moreover, we also compare the complexity of the respective
methods. To this end, we develop the first complexity analysis for the depen­
dency pair approach. While the size­change principle is PSPACE­complete,
we prove that the dependency pair approach (in combination with classical

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

Collections: Computer Technologies and Information Sciences