Example Tree

Tree: $1$ (root) has children $2$ and $3$. Node $2$ has child $4$. DFS walk: Enter $1$ (tin[1]=0, timer becomes $1$), enter $2$ (tin[2]=1, timer becomes $2$), enter $4$ (tin[4]=2, timer becomes $3$), exit $4$ (tout[4]=3), exit $2$ (tout[2]=3), enter $3$ (tin[3]=3, timer becomes $4$), exit $3$ (tout[3]=4), exit $1$ (tout[1]=4).

Subtree of $2$ covers $[1,3)$. Subtree of $1$ covers $[0,4)$. Notice $tin$ values are unique while $tout$ values repeat (tout[4]=tout[2]=3).