Improved Termination Analysis of CHR Using Self-sustainability Analysis

In the past few years, several successful approaches to termination analysis of Constraint Handling Rules (CHR) have been proposed. In parallel to these developments, for termination analysis of Logic Programs (LP), recent work has shown that a stronger focus on the analysis of the cycles in the strongly connected components (SCC) of the program is very beneficial, both for precision and efficiency of the analysis. In this paper we investigate the benefit of using the cycles of the SCCs of CHR programs for termination analysis. It is a non-trivial task to define the notion of a cycle for a CHR program. We introduce the notion of a self-sustaining set of CHR rules and show that it provides a natural counterpart for the notion of a cycle in LP. We prove that non-selfsustainability of an SCC in a CHR program entails termination for all queries to that SCC. Then, we provide an efficient way to prove that an SCC of a CHR program is non-self-sustainable, providing an additional, new way of proving termination of (part of) the program. We integrate these ideas into the CHR termination analyser CHRisTA and demonstrate by means of experiments that this extension significantly improves both the efficiency and the performance of the analyser.