Confluence of Partially Completed Rewrite Systems

Determine whether a partially completed rewrite system generated by Knuth–Bendix completion exhibits sufficient confluence to support greedy application of its rewrite rules.

Background

Knuth–Bendix completion produces a confluent rewrite system when the completion procedure terminates. The paper investigates using generated rewrite rules in a greedy rewriting engine, which applies rules sequentially rather than exploring multiple equivalent terms as equality saturation does.

The authors explicitly hypothesize that confluence-like behavior may persist even when completion is only partial, potentially making greedy rewriting effective without requiring a fully completed rewrite system. The experiments compare the performance of greedy rewriting and equality saturation, but do not establish the claimed confluence property.

References

We hypothesize that a partially completed rewrite system by \ac{KBC} exhibits confluent properties allowing to apply it greedily.

— Augmenting Rewrite Rule Sets via Knuth-Bendix Completion  (2610.01246 - Schifferer et al., 1 Oct 2026) in Section 3, Approach, paragraph beginning “Rewriting Environments.”