Definition. Compositionality, computability, and complexity › Term rewrite systems (§ 6.1) › Confluence (§ 6.1) [pagin2021-confluence]

$\mathrm{\Phi }$ is confluent iff, for all terms $t_1,t_2,t_3$, whenever $t_1{\to }_{\mathrm{\Phi }}^{+}{t}_2$ and $t_1{\to }_{\mathrm{\Phi }}^{+}{t}_3$, there is some $t_4$ such that $t_2{\to }_{\mathrm{\Phi }}^{+}{t}_4$ and $t_3{\to }_{\mathrm{\Phi }}^{+}{t}_4$.