$.  Furthermore, the set of d-separation rules entailed by $G_0$ that is not entailed by $G_0$ is as follows:  -   $X_0$ is d-separated from $X_0$ given $X_0$ or $\{ X_0, Y\}$.  -   $X_0$ is d-separated from $Y  $ given $X_0$ or $\{ X_0, X_0\}$.  -   $X_0$ is d-separated from $Y  $ given $X_0$ or $\{ X_0, X_0\}$.  