Tags:Polynomial Termination, Term Rewriting, Termination and Undecidability

Abstract:

In this paper we prove via a reduction from Hilbert's 10th problem that the problem whether the termination of a given rewrite system can be shown by a polynomial interpretation in the natural numbers is undecidable, even for rewrite systems that are incrementally polynomially terminating. We also prove that incremental polynomial termination is an undecidable property of terminating rewrite systems.