User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-5529393-20130627000838/@comment-5150073-20130627095501

For phi function, I fixed these minor mistakes.

For theta function, let's consider how $$\theta(\Omega^2*2)$$ must be decomposed:

\theta(\Omega^2*2) = \theta(\Omega^2+\Omega^2) = \theta(\Omega^2+\Omega*\Omega) (according to the ruleset A)

Then we make $$\theta(\Omega^2+\Omega*\Omega)[1] = \theta(\Omega^2+\Omega)$$ and $$\theta(\Omega^2+\Omega*\Omega)[n] = \theta(\Omega^2+\Omega*\theta(\Omega^2+\Omega*\Omega)[n-1])$$. So, probably is a good idea to use # instead of $$\alpha$$, as # stand for "a rest of an expression", not a fixed ordinal.