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.

Relation with other properties

Stronger properties

• Strongly confluent rewriting system
• Confluent rewriting system
• Complete rewriting system