# Locally confluent rewriting system

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