[tromp]

The first step proceeds as follow. We want the predecessor of [s,t] with s=[0,0] and t=0.

We first compute s' = P(s) = P([0,0]) = 0. Then in [s',t] = [0,0] we must replace all occurrences of 0 with [0,0], which results in [[0,0],[0,0]]. This is a one-time substitution (else it would never end).

[Hugsun]

Couldn't you also do the substitution n times to make this ordinal emulate the fast growing hierarchy instead of the middle growing one?

[tromp]

Where would you get the number n from? All we have here are binary trees s and t of arbitrary shape.

[wruza]

Ah, now I see, thanks!