Automatic Proofs of Termination With Elementary Interpretations

Abstract

Symbolic constraints arising in proofs of termination of programs are often translated into numeric constraints before checking them for satisfiability. In this setting, polynomial interpretations are a simple and popular choice. In the nineties, Lescanne introduced the elementary algebraic interpretations as a suitable alternative to polynomial interpretations in proofs of termination of term rewriting. Here, not only addition and product but also exponential expressions are allowed. Lescanne investigated the use of elementary interpretations for witnessing satisfiability of a given set of symbolic constraints. He also motivated the usefulness of elementary interpretations in proofs of termination by means of several examples. Unfortunately, he did not consider the automatic generation of such interpretations for a given termination problem. This is an important drawback for using these interpretations in practice. In this paper we show how to solve this problem by using a combination of rewriting, CLP, and CSP techniques for handling the elementary constraints which are obtained when giving the symbols parametric elementary interpretations.