Loops under Strategies ... Continued

TL;DR

This paper develops decision procedures to determine whether loops in term rewrite systems also imply non-termination under specific evaluation strategies, extending previous work to more complex strategies.

Contribution

It introduces new decision procedures for analyzing loops under strategies like leftmost-innermost and parallel evaluation, enabling automatic non-termination proofs.

Findings

First approach to automatically disprove termination under these strategies

Decision procedures for multiple complex strategies developed

Extends previous work on innermost, outermost, and context-sensitive strategies

Abstract

While there are many approaches for automatically proving termination of term rewrite systems, up to now there exist only few techniques to disprove their termination automatically. Almost all of these techniques try to find loops, where the existence of a loop implies non-termination of the rewrite system. However, most programming languages use specific evaluation strategies, whereas loop detection techniques usually do not take strategies into account. So even if a rewrite system has a loop, it may still be terminating under certain strategies. Therefore, our goal is to develop decision procedures which can determine whether a given loop is also a loop under the respective evaluation strategy. In earlier work, such procedures were presented for the strategies of innermost, outermost, and context-sensitive evaluation. In the current paper, we build upon this work and develop such decision procedures for important strategies like leftmost-innermost, leftmost-outermost, (max-)parallel-innermost, (max-)parallel-outermost, and forbidden patterns (which generalize innermost, outermost, and context-sensitive strategies). In this way, we obtain the first approach to disprove termination under these strategies automatically.