A Terminating and Confluent Term Rewriting System for the Pure Equational Theory of Quandles

Abstract

This article presents a term rewriting system for the first-order equational theory of quandles that is both terminating and confluent. As a consequence, it has unique normal forms and so encodes a decision procedure for quandle identities. However, the problem of computing a normal form for this term rewriting system is, in worst case, EXP hard.