SAT Solving for Argument Filterings

TL;DR

This paper presents a SAT-based encoding for lexicographic path orders and argument filterings to improve termination analysis of term rewrite systems, resulting in significant speedups and enhanced proving capabilities.

Contribution

It introduces a novel propositional encoding for argument filterings in lexicographic path orders, enabling efficient SAT-based termination analysis.

Findings

Order of magnitude speedups in termination proofs

Increased termination proving power with SAT encoding

Effective integration into the AProVE termination prover

Abstract

This paper introduces a propositional encoding for lexicographic path orders in connection with dependency pairs. This facilitates the application of SAT solvers for termination analysis of term rewrite systems based on the dependency pair method. We address two main inter-related issues and encode them as satisfiability problems of propositional formulas that can be efficiently handled by SAT solving: (1) the combined search for a lexicographic path order together with an \emph{argument filtering} to orient a set of inequalities; and (2) how the choice of the argument filtering influences the set of inequalities that have to be oriented. 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.