Summary: Proving Termination using Recursive
Path Orders and SAT Solving #
Peter Schneider­Kamp 1 , Ren’e Thiemann 1 , Elena Annov 2 ,
Michael Codish 2 , and J˜urgen Giesl 1
1 LuFG Informatik 2, RWTH Aachen, Germany,
{psk,thiemann,giesl}@informatik.rwth­aachen.de
2 Department of Computer Science, Ben­Gurion University, Israel,
{annov,mcodish}@cs.bgu.ac.il
Abstract. We introduce a propositional encoding of the recursive path
order with status (RPO). RPO is a combination of a multiset path order
and a lexicographic path order which considers permutations of the argu­
ments in the lexicographic comparison. Our encoding allows us to apply
SAT solvers in order to determine whether a given term rewrite system
is RPO­terminating. Furthermore, to apply RPO within the dependency
pair framework, we combined our novel encoding for RPO with an exist­
ing encoding for argument filters. We implemented our contributions in
the termination prover AProVE. Our experiments show that due to our
encoding, combining termination provers with SAT solvers improves the
performance of RPO­implementations by orders of magnitude.
1 Introduction

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

Collections: Computer Technologies and Information Sciences