Strongly confluent rewriting system

Symbol-free definition
A rewriting system is said to be strongly confluent if it satisfies the following two conditions:


 * 1) It is a locally strongly confluent rewriting system: Whenever $$u \to v$$ and $$u \to w$$ are (one-step) reductions, then there is a $$z$$ and one-step reductions $$v \to z$$ and $$w \to z$$.
 * 2) It is a finitely terminating rewriting system: Any chain of reductions must terminate in finitely many steps.

An alternative way of saying that a rewriting system is strongly confluent is that it has the Church-Rosser property.

Weaker properties

 * Confluent rewriting system is the corresponding property for multi-step reductions. The fact that any strongly confluent rewriting system is confluent has a neat diagrammatic proof which involves completion of squares.