User blog comment:Rgetar/Ordinal Explorer Online/@comment-31040770-20200218051121/@comment-32213734-20200218123204

I checked it, and I think that it is all right.

Agree, it looks pretty weird. I'll explain, what's going on here:
 * [c + I] = Φ(1, 0)
 * [L + I·[L][c + I]] = [L + I·[L]Φ(1, 0)]

(where [L]Φ(1, 0) is booster-base expression, not [L] multiplied by Φ(1, 0)) Booster of this expression:
 * [I + [L]Φ(1, 0)]L = L + ωI + [L]Φ(1, 0) = L + I·[L]Φ(1, 0)

Booster of this expression:
 * [[L]Φ(1, 0)]I = I + ω[L]Φ(1, 0) = I + [L]Φ(1, 0)

And booster of this expression:
 * [L]Φ(1, 0)

Its cofinality is ω, and its cofinality and fs is calculated using "cascade" rule, that is it is transformed into
 * [I]Φ(1, 0)

then "cascade" rule is used once again, and it is transformed into
 * [Φ(1, 0)]Φ(1, 0) = Φ(1, 0) + ωΦ(1, 0) = Φ(1, 0)2

(It is like transformation [L] → [I] → [Φ(1, 0)], but this time it is not visible in "minimized" mode, since "[L]Φ(1, 0)" part of the expression is minimized, not the whole expression "[L + I·[L]Φ(1, 0)]").

Fundamental sequence of Φ(1, 0):
 * 1
 * Ωω
 * ΩΩ ω
 * ΩΩ Ω ω
 * ΩΩ Ω Ω ω

So, transformations:
 * [L]Φ(1, 0) → Φ(1, 0)2
 * [[L]Φ(1, 0)]I → [Φ(1, 0)2]I = I + ωΦ(1, 0)2 = I + Φ(1, 0)2
 * [[[L]Φ(1, 0)]I]L → [I + Φ(1, 0)2]L = L + ωI + Φ(1, 0) 2 = L + I·Φ(1, 0)Φ(1, 0)
 * [L + I·[L]Φ(1, 0)] → [L + I·Φ(1, 0)Φ(1, 0)]

And its fundamental sequence:
 * [L + I·Φ(1, 0)ω] = [[[Φ(1, 0) + 1]I]L] = [[I + ωΦ(1, 0) + 1]L] = [[I + Φ(1, 0)ω]L] = [L + ωI + Φ(1, 0)ω]
 * [L + I·Φ(1, 0)Ωω]
 * [L + I·Φ(1, 0)ΩΩ ω]
 * [L + I·Φ(1, 0)ΩΩ Ω ω]
 * [L + I·Φ(1, 0)ΩΩ Ω Ω ω]