# Polytool: polynomial interpretations as a basis for termination analysis of Logic programs

## TL;DR

Polytool introduces a novel approach to logic program termination analysis by adapting polynomial interpretations from term rewriting systems, enabling more general and automated analysis techniques.

## Contribution

The paper presents the first adaptation of polynomial interpretations for termination analysis of logic programs, including a new constraint-based method and implementation.

## Key findings

- Successfully generalized termination analysis techniques to arbitrary polynomials.
- Developed an automatic tool, Polytool, for logic program termination analysis.
- Extended standard concepts of termination analysis to polynomial interpretations.

## Abstract

Our goal is to study the feasibility of porting termination analysis techniques developed for one programming paradigm to another paradigm. In this paper, we show how to adapt termination analysis techniques based on polynomial interpretations - very well known in the context of term rewrite systems (TRSs) - to obtain new (non-transformational) ter- mination analysis techniques for definite logic programs (LPs). This leads to an approach that can be seen as a direct generalization of the traditional techniques in termination analysis of LPs, where linear norms and level mappings are used. Our extension general- izes these to arbitrary polynomials. We extend a number of standard concepts and results on termination analysis to the context of polynomial interpretations. We also propose a constraint-based approach for automatically generating polynomial interpretations that satisfy the termination conditions. Based on this approach, we implemented a new tool, called Polytool, for automatic termination analysis of LPs.