nLab locally confluent

Let (X,)(X,\rightarrow) be an abstract rewriting system ie. a set equipped with a binary relation \rightarrow. Write *\rightarrow^{*} for the reflexive-transitive closure of \rightarrow. We say that \rightarrow is locally confluent iff for every a,b,cXa,b,c \in X such that aba \rightarrow b and aca \rightarrow c, there exists dXd \in X such that b *db \rightarrow^{*} d and c *dc \rightarrow^{*} d.

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