Locally confluent rewriting system

Definition
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 $$w \longrightarrow z$$.

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

Stronger properties

 * Weaker than::Strongly confluent rewriting system
 * Weaker than::Confluent rewriting system
 * Weaker than::Complete rewriting system