User blog comment:P進大好きbot/New Googological Ruler/@comment-39541634-20190722124029/@comment-35470197-20190723114656

> In fairness, though, a simplifed OCF can often be equivalent to the original.

Yeah, exactly. This is just my guess from the result ψ^{Ω_1}(ε_{M+1}) = PTO(KPM) = ψ_{Ω_1}(ψ_{χ_{M+1}(0)}(0)) << ψ_{Ω_1}(M) << ψ_{Ω_1}(ε_{M+1}). The limits of these notations can coincide with each other.

> You just need to be careful when you simplify, not to throw away the wrong stuff :-)

Honestly, I am not good at simplifying existing stuffs. Since I tend to require myself a proof of the comparison, I usually create systems more complicated than the original ones so that I can easily verify the comparison.

More precisely, I personally think that simplifying strong notations is very difficult, and is one of central topics in computable googology, for which I really need more experiences. Therefore I rarely simplify existing OCFs.