Comparing CSP and SAT Solvers for Polynomial Constraints in Termination Provers

Proofs of termination in term rewriting involve solving constraints between terms coming from (parts of) the rules of the term rewriting system. A common way to deal with such constraints in termination tools is treating them as polynomial constraints. Several recent works develop connections between these problems and more standard constraint solving problems for which well-known and efficient techniques apply. In particular, SAT techniques are receiving increasing attention in the field. The main idea is encoding polynomial constraints as propositional constraints which can (hopefully) be efficiently managed by using state-of-the-art SAT solvers. We have recently developed an algorithm for solving constraints in finite (small) domains of coefficients which are appropriate for termination tools. This algorithm benefits from the use of a specialized representation of the elements in the domain and the corresponding polynomials which permits using efficient arithmetics and constraint propagation techniques. In this paper we discuss these approaches, compare them from an experimental point of view, and point to possible improvements.