# Locally confluent rewriting system

From Groupprops

Template:Rewriting system property

## Definition

A rewriting system is said to be **confluent** if it satisfies the following condition: whenever and are *one*-step reductions in the rewriting system, then there exists a word such that there exist multi-step reductions and .

In other words, any two things obtained by single-step reductions from the same source finally get together again.