Implementing RPO and POLO using SAT

Carsten Fuhs, Peter Schneider-Kamp, Rene Thiemann, Jürgen Giesl, Elena Annov, Michael Codish, Aart Middeldorp, Harald Zankl

Research output: Contribution to journalConference articlepeer-review


Well-founded orders are the most basic, but also most important ingredient to virtually all termination analyses. Numerous fully automated search algorithms for these classes have therefore been devised and implemented in termination tools. Unfortunately, for termination problems occurring in practice, the performance of existing algorithms is often insufficient. Performance can be improved significantly by reducing these search problems to decision problems for which more efficient algorithms already exist. Here, we introduce an encoding of RPO and POLO to the satisfiability of propositional logic (SAT). We implemented these encodings in our termination tool AProVE. Extensive experiments have shown that one can obtain speedups in orders of magnitude by this encoding and the application of modern SAT solvers.

Original languageEnglish
JournalDagstuhl Seminar Proceedings
StatePublished - 1 Jan 2007
EventDeduction and Decision Procedures 2007 - Wadern, Germany
Duration: 30 Sep 20075 Oct 2007


  • SAT solving
  • dependency pairs
  • polynomial interpretation
  • recursive path order
  • term rewriting
  • termination

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Control and Systems Engineering


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