Abstract

Polynomial interpretations are a useful technique for proving termination
of term rewrite systems. In an automated setting, termination tools are
concerned with parametric polynomials whose coefficients (i.e., the
parameters) are initially unknown and have to be instantiated suitably
such that the resulting concrete polynomials satisfy certain conditions.
We focus on monotonicity and well-definedness, the two main conditions
that are independent of the respective term rewrite system considered,
and provide constraints on the abstract coefficients for linear,
quadratic and cubic parametric polynomials such that monotonicity and
well-definedness of the resulting concrete polynomials are guaranteed
whenever the constraints are satisfied. Our approach subsumes the
absolute positiveness approach, which is currently used in many
termination tools. In particular, it allows for negative numbers in
certain coefficients. We also give an example of a term rewrite system
whose termination proof relies on the use of negative coefficients, thus
showing that our approach is more powerful.

BibTeX

@inproceedings{FNHZAM-IJCAR10,
  author      = "Friedrich Neurauter and Harald Zankl and Aart Middeldorp",
  title       = "Monotonicity Criteria for Polynomial Interpretations over
                 the Naturals",
  booktitle   = "Proceedings of the 5th International Joint Conference on
                 Automated Reasoning",
  series      = "Lecture Notes in Artificial Intelligence",
  volume      = 6173,
  pages       = "502--517",
  publisher   = "Springer-Verlag",
  year        = 2010
}