Church-Rosser property

Let $R$ be a binary relation that is reflexive and transitive. We say that $R$ has the diamond property if, whenever $X~R~Y$ and $X~R~Z$, then there is a $W$ such that $Y~R~W$ and $Z~R~W$. If a relation $R$ has the diamond property, we say that $R$ is Church-Rosser.