Canonizer non-overlap versus rewriting orthogonality

Investigate and precisely characterize the relationship between the non-overlapping criterion used to construct canonizers in equational reasoning and orthogonality in term rewriting systems; derive formal conditions that connect or distinguish these notions.

Background

The paper defines canonizers for equational laws and introduces a non-overlapping criterion to ensure they produce invariants. The authors observe similarities between this criterion and orthogonality in rewriting systems.

They explicitly leave for future work the precise investigation of this relationship, suggesting potential theoretical unification or clarification within the framework of term rewriting.

References

Though we note that the non-overlapping criterion seems very similar to the notion of orthogonality in rewriting, we leave the investigation of the precise relationship of the classical theory with the above technique as future work.

— The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale (2512.07087 - Bolan et al., 8 Dec 2025) in Section Canonization (Syntactic arguments, Subsection Canonization)