Which ordinals correspond to reduction graphs in the -calculus?

The source page states the original problem together with its recorded qualifications and progress updates as follows.

Some reduction graphs in $\lambda$-calculus [Venturini-Zilli, 1991] are isomorphic to ordinals. For example, the reduction graph of $(\lambda x.y)((\lambda z.zzz)(\lambda z.zzz))$ is isomorphic to $\omega + 1$. Which ordinals appear in this way as reduction graphs? It is known that all ordinals less than $\epsilon_0$ can be so represented.