A Method to Prove the Positiveness of Polynomials

Abstract

Termination is an important property for programming and particularly for term rewriting systems. The well-known polynomial orderings can be used for proving the termination of term rewriting systems. The proof of the positiveness of a polynomial presents a crucial point concerning polynomial orderings. There exists a powerful non-deterministic method for performing such proofs that has been developed by BenCherifa and Lescanne. We describe some observations on the time complexity of this approach. In addition, a deterministic version is presented which has the same power as the original one. We also deal with a modification for signatures which do not contain any constant symbols. Finally, we discuss an improvement of the non-deterministic method.