Critical pair (term rewriting)

In the context of term rewriting systems (TRS), a **critical pair** is a fundamental concept used to analyze and verify properties of the rewrite system, particularly concerning confluence—a property that ensures that the final result of rewriting a term is independent of the order in which the rewriting steps are applied. To understand critical pairs, we first need to consider how term rewriting works. A term rewriting system consists of a set of rules that define how terms can be transformed.