SAT solving for termination proofs with recursive path orders and dependency pairs

Michael Codish, Jürgen Giesl, Peter Schneider-Kamp, René Thiemann

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


This paper introduces a propositional encoding for recursive path orders (RPO), in connection with dependency pairs. Hence, we capture in a uniform setting all common instances of RPO, i.e.; lexicographic path orders (LPO), multiset path orders (MPO), and lexicographic path orders with status (LPOS). This facilitates the application of SAT solvers for termination analysis of term rewrite systems (TRSs). We address four main inter-related issues and show how to encode them as satisfiability problems of propositional formulas that can be efficiently handled by SAT solving: (A) the lexicographic comparison w.r.t. a permutation of the arguments; (B) the multiset extension of a base order; (C) the combined search for a path order together with an argument filter to orient a set of inequalities; and (D) how the choice of the argument filter influences the set of inequalities that have to be oriented (so-called usable rules). We have implemented our contributions in the termination prover AProVE. Extensive experiments show that by our encoding and the application of SAT solvers one obtains speedups in orders of magnitude as well as increased termination proving power.

Original languageEnglish
Pages (from-to)53-93
Number of pages41
JournalJournal of Automated Reasoning
Issue number1
StatePublished - 1 Jun 2012


  • Dependency pairs
  • Recursive path order
  • SAT solving
  • Term rewriting
  • Termination

ASJC Scopus subject areas

  • Software
  • Computational Theory and Mathematics
  • Artificial Intelligence


Dive into the research topics of 'SAT solving for termination proofs with recursive path orders and dependency pairs'. Together they form a unique fingerprint.

Cite this