Proving Termination Using Recursive Path Orders and SAT Solving

Authors:
Peter Schneider-Kamp;René Thiemann;Elena Annov;Michael Codish;Jürgen Giesl
Affiliations:
LuFG Informatik 2, RWTH Aachen, Germany;LuFG Informatik 2, RWTH Aachen, Germany;Department of Computer Science, Ben-Gurion University, Israel;Department of Computer Science, Ben-Gurion University, Israel;LuFG Informatik 2, RWTH Aachen, Germany
Venue:
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Year:
2007

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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 arguments in the lexicographic comparison. Our encoding allows us to apply SAT solvers in order to determine whether a given term rewrite system is RPO-terminating. Furthermore, to apply RPO within the dependency pair framework, we combined our novel encoding for RPO with an existing 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 RPO-implementations by orders of magnitude.