Here’re the comparisons between sDAN and Taranovsky’s ordinal notation.

Fundamental sequences: Let L(α) be the amount of C’s in standard representation of α, then ${\alpha[n]=\max\{\beta|\beta<\alpha\land L(\beta)\le L(\alpha)+n\}}$ .

Up to {1,,`1,,`2^,,}

In last post, I showed that C(Ω₂2,0) works as the 1-separator in C(Ω₂+____,β), but it’s C(Ω₂+C(Ω₂,C(Ω₂2,0)),0) that works as the 1-separator in C(Ω₂+C(C(Ω₂2+____,0),C(Ω₂2,0)),β). And, C(Ω₂,C(Ω₂2,0)) works as the 2-separator in C(Ω₂+____,β).

Up to a C(Ω₂,C(Ω₂,C(Ω₂2,0)))

Now let ordinal σ = C(Ω₂2,0). And α⁺ is shorthand for C(Ω₂,α).

{1{1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺,σ⁺),0),0),0) (`,, is the 1-separator on the double comma)
{1{1{1`,,2^,,}2}2{1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺,σ⁺),0)2,0),0)
{1,,2{1`,,2^,,}2} has recursion level C(C(Ω₂2+C(C(Ω₂+C(σ⁺⁺,σ⁺),0)⁺,C(Ω₂+C(σ⁺⁺,σ⁺),0)),0),0)
{1,,1,,2{1`,,2^,,}2} has recursion level C(C(Ω₂2+C(σ,C(Ω₂+C(σ⁺⁺,σ⁺),0)),0),0)
{1,,1,,1,,2{1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺+σ,C(Ω₂+C(σ⁺⁺,σ⁺),0)),0),0)
{1{1,,2^,,}2{1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺+σ),C(Ω₂+C(σ⁺⁺,σ⁺),0)),0),0)
{1{1,,1,,2^,,}2{1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+ω^ω^(σ⁺+σ),C(Ω₂+C(σ⁺⁺,σ⁺),0)),0),0)
{1{1{1,,2^,,}2^,,}2{1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+ω^ω^ω^(σ⁺+σ),C(Ω₂+C(σ⁺⁺,σ⁺),0)),0),0)
{1{1`,,2^,,}3} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺,σ⁺),C(Ω₂+C(σ⁺⁺,σ⁺),0)),0),0)
{1{1`,,2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺,σ⁺)+1,0),0),0)
{1{1`,,2^,,}1,,2} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺,σ⁺)+σ,0),0),0)
{1{1`,,2^,,}1,,1,,2} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺,σ⁺)+σ⁺+σ,0),0),0)
{1{1`,,2^,,}1{1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺,σ⁺)2,0),0),0)
{1{2`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(C(σ⁺⁺,σ⁺)+1),0),0),0)
{1,,2`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(C(σ⁺⁺,σ⁺)+σ),0),0),0)
{1,,1,,2`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(C(σ⁺⁺,σ⁺)+σ⁺+σ),0),0),0)
{1{1`,,2^,,}2`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(C(σ⁺⁺,σ⁺)2),0),0),0)
{1{1`,,2^,,}1{1`,,2^,,}2`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^ω^(C(σ⁺⁺,σ⁺)2),0),0),0)
{1{1{1`,,2^,,}2`,,2^,,}2`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^ω^ω^(C(σ⁺⁺,σ⁺)2),0),0),0)
{1`,,3^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺,C(σ⁺⁺,σ⁺)),0),0),0)
{1`,,1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺+1,σ⁺),0),0),0)
{1`,,1{1`,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺+C(σ⁺⁺,σ⁺),σ⁺),0),0),0)
{1`,,1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺2,σ⁺),0),0),0)
{1{2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(ω^(σ⁺⁺+1),σ⁺),0),0),0)
{1{1`,,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(ω^(σ⁺⁺2),σ⁺),0),0),0)
{1{1{1`,,2^`,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(ω^ω^ω^(σ⁺⁺2),σ⁺),0),0),0)
{1{1` `,,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺⁺,σ⁺),0),0),0) (` `,, is the 1-separator on the `,,)
{1,,`1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+1,σ),σ⁺),0),0),0) (,,` is the 2-separator on the double comma)
{1,,`1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ,σ),σ⁺),0),0),0)
{1{1,,`1{1{1,,`1,,2^,,}2}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ,σ),σ⁺)+1,0),0),0)
{1{1,,`1{1{1,,`1,,2^,,}2}2^,,}1{1,,`1,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ,σ),σ⁺)+C(C(Ω₂+1,σ),σ⁺),0),0),0)
{1{1,,`1{1{1,,`1,,2^,,}2}2^,,}1{1,,`1{1{1,,`1,,2^,,}2}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ,σ),σ⁺)2,0),0),0)
{1{2{1,,`1{1{1,,`1,,2^,,}2}2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(C(C(Ω₂+σ,σ),σ⁺)+1),0),0),0)
{1`,,2{1,,`1{1{1,,`1,,2^,,}2}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺,C(C(Ω₂+σ,σ),σ⁺)),0),0),0)
{1{1,,`1{1{1,,`1,,2^,,}2}2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ,σ)+1,σ⁺),0),0),0)
{1{1,,`1,2^,,}2,,`1{1{1,,`1,,2^,,}2}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ,σ)+C(Ω₂+1,σ),σ⁺),0),0),0)
{1{1,,`1{1{1,,`1,,2^,,}2}2^,,}2,,`1{1{1,,`1,,2^,,}2}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ,σ)2,σ⁺),0),0),0)
{1,,`2{1{1,,`1,,2^,,}2}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ,σ)⁺,σ⁺),0),0),0)
{1,,`1{1{1,,`1,,2^,,}2}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ+1,σ),σ⁺),0),0),0)
{1,,`1{1{1,,`1,,2^,,}2}1{1{1,,`1,,2^,,}2}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ2,σ),σ⁺),0),0),0)
{1,,2{1,,`1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(σ⁺,σ),σ),σ⁺),0),0),0)
{1,,1,2{1,,`1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+1,σ),σ),σ),σ⁺),0),0),0)
{1,,1{1{1,,`1,,2^,,}2}2{1,,`1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+σ,σ),σ),σ),σ⁺),0),0),0)
{1,,1{1,,2{1,,`1,,2^,,}2}2{1,,`1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+σ⁺,σ),σ),σ),σ⁺),0),0),0)
{1,,1{1{1,,1,2{1,,`1,,2^,,}2}2,,2{1,,`1,,2^,,}2}2{1,,`1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+C(C(Ω₂+1,σ),σ⁺),σ),σ),σ),σ⁺),0),0),0)
{1,,1{1{1,,1{1{1,,`1,,2^,,}2}2{1,,`1,,2^,,}2}2,,2{1,,`1,,2^,,}2}2{1,,`1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+C(C(Ω₂+σ,σ),σ⁺),σ),σ),σ),σ⁺),0),0),0)
{1,,1{1{1,,1{1,,2{1,,`1,,2^,,}2}2{1,,`1,,2^,,}2}2,,2{1,,`1,,2^,,}2}2{1,,`1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂2,σ),σ),σ),σ⁺),0),0),0)
{1,,2{1{1,,1{1,,2{1,,`1,,2^,,}2}2{1,,`1,,2^,,}2}2,,2{1,,`1,,2^,,}2}2{1,,`1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂2,σ)⁺,σ),σ),σ⁺),0),0),0)
{1,,1{1{1,,1{1,,2{1,,`1,,2^,,}2}2{1,,`1,,2^,,}2}2,,2{1,,`1,,2^,,}2}1,2{1,,`1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂2+1,0),σ),σ),σ⁺),0),0),0)
{1,,1{1{1,,1{1,,2{1,,`1,,2^,,}2}2{1,,`1,,2^,,}2}2,,2{1,,`1,,2^,,}2}1{1{1,,`1{1{1,,`1,,2^,,}2}2^,,}2}2{1,,`1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ,σ),σ⁺),0),0),σ),σ),σ⁺),0),0),0)
{1,,1{1{1,,1{1,,2{1,,`1,,2^,,}2}2{1,,`1,,2^,,}2}2,,2{1,,`1,,2^,,}2}1{1{1,,`1,,2^,,}2}2{1,,`1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺,σ),σ⁺),0),0),0)
{1{1,,`1,,2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺,σ),σ⁺)+1,0),0),0)
{1`,,2{1,,`1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺,C(C(Ω₂+σ⁺,σ),σ⁺)),0),0),0)
{1{1,,`1,,2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺,σ)+1,σ⁺),0),0),0)
{1{1,,`1,2^,,}2,,`1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺,σ)+C(Ω₂+1,σ),σ⁺),0),0),0)
{1,,`2,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺,σ)⁺,σ⁺),0),0),0)
{1,,`1,,1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺+1,σ),σ⁺),0),0),0)
{1,,`1{1`,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(σ⁺⁺,σ⁺),σ),σ⁺),0),0),0)
{1,,`1{1{1,,`1,2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+1,σ),σ⁺),σ),σ⁺),0),0),0)
{1,,`1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1{1,,`1`,,2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺)+1,0),0),0)
{1`,,2{1,,`1`,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺,C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1`,,2^,,}3^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1`,,2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ)+1,σ⁺),0),0),0)
{1{1,,`1`,,2^,,}2,,`1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ)2,σ⁺),0),0),0)
{1,,`2`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ)⁺,σ⁺),0),0),0)
{1,,`1{1,,`2`,,2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂2,σ)⁺,σ⁺),C(Ω₂2,σ)),σ⁺),0),0),0)
{1,,`1`,,3^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,C(Ω₂2,σ)),σ⁺),0),0),0)
{1,,`1`,,1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+1,0),σ⁺),0),0),0)
{1,,`1`,,1{1{2^,,}2}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+C(Ω₂+ω^(σ⁺+1),0),0),σ⁺),0),0),0)
{1,,`1`,,1{1{1,,`1`,,1,2^,,}2}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+1,0),σ⁺),0),0),σ⁺),0),0),0)
{1,,`1`,,1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),0)

So here comes a further guess: does C(Ω₂+C(Ω₂,C(Ω₂,C(Ω₂2,0))),0) work as the 2-separator in C(Ω₂+C(C(Ω₂2+____,0),C(Ω₂2,0)),β)?

Up to a C(Ω₂,C(Ω₂,C(Ω₂,C(Ω₂2,0))))

Now let separator ♦ = {1{1,,`1`,,1,,2^,,}2} and let ordinal σ = C(Ω₂2,0). And α⁺ is shorthand for C(Ω₂,α).

{1,,1{1{1{1,,`1`,,1♦2^,,}2}2,,1{1,,1,,2}2}2{1,,1,,2}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),0)
{1,,1{1{1{1,,`1`,,1♦2^,,}2}2,,1{1,,1,,2}2}1{1{1{1,,`1`,,1♦2^,,}2}2,,1{1,,1,,2}2}2{1,,1,,2}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),C(Ω₂+σ,0)),0),0)
{1,,1{1{1{1,,`1`,,1♦2^,,}2}1,2,,1{1,,1,,2}2}2{1,,1,,2}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0)+1,C(Ω₂+σ,0)),0),0)
{1{1,,1{1{1,,`1`,,1♦2^,,}2}2}2,,1{1{1,,`1`,,1♦2^,,}2}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0)2,C(Ω₂+σ,0)),0),0)
{1,,2{1{1,,`1`,,1♦2^,,}2}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0)⁺,C(Ω₂+σ,0)),0),0)
{1,,1{1,,1{1{1,,`1`,,1♦2^,,}2}2}1,2{1{1,,`1`,,1♦2^,,}2}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+1,0),C(Ω₂+σ,0)),0),0)
{1,,1{1,,1{1{1,,`1`,,1♦2^,,}2}2}1{1,,2{1,,1,,2}2}2{1{1,,`1`,,1♦2^,,}2}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+σ,0)⁺,0),0)
{1,,1{1,,1{1{1,,`1`,,1♦2^,,}2}2}1{1,,1{1{1,,`1`,,1♦2^,,}2}2}2{1{1,,`1`,,1♦2^,,}2}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ),0),0),0)
{1,,1{2{1,,`1`,,1♦2^,,}2}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+ω^(C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ)+1),0),0),0)
{1{1,,1,,2}2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+ω^(C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ)+σ),0),0),0)
{1{1,,1,,1,2}2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+σ⁺+1,0),0),0)
{1{1,,1,,1,,1,2}2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+σ⁺2+1,0),0),0)
{1{1{1`,,2^,,}2}2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(σ⁺⁺,σ⁺),0),0),0)
{1{1{1,,`1,2^,,}2}2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂+1,σ),σ⁺),0),0),0)
{1{1{1,,`1`,,2^,,}2}2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1{1{1,,`1`,,1,2^,,}2}2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+1,0),σ⁺),0),0),0)
{1{1{1,,`1`,,1♦2^,,}2}2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0),0),0)
{1{1{1,,`1`,,1♦2^,,}2}1,2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+ω^(C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0)+1),0),0)
{1,,2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0)⁺,C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0)),0),0)
{1,,1,,2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(σ,C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0)),0),0)
{1,,1{1,,2,,2{1,,`1`,,1♦2^,,}2}1{1,,1,,2{1,,`1`,,1♦2^,,}2}2,,2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(Ω₂2+C(Ω₂+σ⁺,C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0)),σ),C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0)),0),0)
{1,,1,,1,2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(Ω₂2+C(Ω₂+σ⁺+1,C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0)),σ),C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0)),0),0)
{1,,1,,1,,2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(Ω₂2+C(Ω₂+σ⁺+σ,C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0)),σ),C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0)),0),0)
{1{1,,`1`,,1,2^,,}2{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(Ω₂2+C(Ω₂+C(C(Ω₂2+1,0),σ⁺),C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0)),σ),C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0)),0),0)
{1{1,,`1`,,1♦2^,,}3} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ),C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0)),0),0)
{1{1{1,,`1`,,1♦2^,,}3}2{1,,`1`,,1♦2^,,}3} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0)),0),0)
{1{1,,`1`,,1♦2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺)+1,0),0),0)
{1{1,,`1`,,1♦2^,,}1,,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺)+σ,0),0),0)
{1{1,,`1`,,1♦2^,,}1,,1,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺)+σ⁺+1,0),0),0)
{1{1,,`1`,,1♦2^,,}1{1,,`1`,,1,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺)+C(C(Ω₂2+1,0),σ⁺),0),0),0)
{1{1,,`1`,,1♦2^,,}1{1,,`1`,,1{1{1,,`1`,,1♦2^,,}2}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺)+C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0),0),σ⁺),0),0),0)
{1{1,,`1`,,1♦2^,,}1{1,,`1`,,1♦2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺)2,0),0),0)
{1{2{1,,`1`,,1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+ω^(C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺)+1),0),0),0)
{1`,,2{1,,`1`,,1♦2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(σ⁺⁺,C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺)),0),0),0)
{1{1,,`1,,1,2^,,}2{1,,`1`,,1♦2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂+σ⁺+1,σ),C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺)),0),0),0)
{1{1,,`1`,,2^,,}2{1,,`1`,,1♦2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2,σ),C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺)),0),0),0)
{1{1,,`1`,,1♦2^,,}3^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺)),0),0),0)
{1{1,,`1`,,1♦2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0)+1,σ⁺),0),0),0)
{1{1,,`1,2^,,}2,,`1`,,1♦2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0)+C(Ω₂+1,σ),σ⁺),0),0),0)
{1{1,,`1`,,1♦2^,,}2,,`1`,,1♦2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0)2,σ⁺),0),0),0)
{1,,`2`,,1♦2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0)⁺,σ⁺),0),0),0)
{1,,`1`,,2♦2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2,C(Ω₂2+C(Ω₂+σ⁺⁺,0),0)),σ⁺),0),0),0)
{1,,`1`,,1♦1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+1,0),σ⁺),0),0),0)
{1,,`1`,,1♦1{1{1,,`1`,,1♦2^,,}2}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0),0),σ⁺),0),0),0)
{1,,`1`,,1♦1♦2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)2,0),0)
{1,,2{1,,`1`,,1,,2^,,}2} has recursion level C(C(Ω₂2+C(C(Ω₂+σ⁺⁺,0)⁺,C(Ω₂+σ⁺⁺,0)),0),0)
{1,,1,,2{1,,`1`,,1,,2^,,}2} has recursion level C(C(Ω₂2+C(σ,C(Ω₂+σ⁺⁺,0)),0),0)
{1,,1,,1,,2{1,,`1`,,1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺+σ,C(Ω₂+σ⁺⁺,0)),0),0)
{1{1`,,2^,,}2{1,,`1`,,1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺,σ⁺),C(Ω₂+σ⁺⁺,0)),0),0)
{1{1,,`1,2^,,}2{1,,`1`,,1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+1,σ),σ⁺),C(Ω₂+σ⁺⁺,0)),0),0)
{1{1,,`1,,1,2^,,}2{1,,`1`,,1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺+1,σ),σ⁺),C(Ω₂+σ⁺⁺,0)),0),0)
{1{1,,`1{1{1,,`1,2^,,}2^,,}2^,,}2{1,,`1`,,1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+1,σ),σ⁺),σ),σ⁺),C(Ω₂+σ⁺⁺,0)),0),0)
{1{1,,`1`,,2^,,}2{1,,`1`,,1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺),C(Ω₂+σ⁺⁺,0)),0),0)
{1{1,,`1`,,1,2^,,}2{1,,`1`,,1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+1,0),σ⁺),C(Ω₂+σ⁺⁺,0)),0),0)
{1{1,,`1`,,1{1{1,,`1`,,1♦2^,,}2}2^,,}2{1,,`1`,,1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0),0),σ⁺),C(Ω₂+σ⁺⁺,0)),0),0)
{1{1,,`1`,,1♦2^,,}2{1,,`1`,,1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),C(Ω₂+σ⁺⁺,0)),0),0)
{1{1,,`1`,,1{1,,2{1,,`1`,,1,,2^,,}2}2^,,}2{1,,`1`,,1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0)⁺,0),σ⁺),C(Ω₂+σ⁺⁺,0)),0),0)
{1{1,,`1`,,1,,2^,,}3} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,C(Ω₂+σ⁺⁺,0)),0),0)
{1{1,,`1`,,1,,2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+1,0),0),0)

As shown above, C(Ω₂+C(Ω₂,C(Ω₂,C(Ω₂2,0))),0) is not so strong as I originally conjectured – it just works as the 1-separator in C(Ω₂+C(C(Ω₂2+____,0),C(Ω₂,C(Ω₂2,0))),β), and corresponds to {1{1,,`1`,,1,,2^,,}2}.

Now let ordinal σ = C(Ω₂2,0). And α⁺ is shorthand for C(Ω₂,α).

{1{1,,`1`,,1,,2^,,}1,,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+σ,0),0),0)
{1{1,,`1`,,1,,2^,,}1{1{1,,`1`,,1,,2^,,}1,,2}1{1{1,,`1`,,1,,2^,,}1,,2}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+σ2,0),0),0)
{1,,2{1,,`1`,,1,,2^,,}1,,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+C(σ⁺,σ),0),0),0)
{1,,1{1{1,,`1`,,1,,2^,,}1,,2}2{1,,`1`,,1,,2^,,}1,,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+C(C(Ω₂+σ,σ),σ),0),0),0)
{1,,1{1,,2{1,,`1`,,1,,2^,,}1,,2}2{1,,`1`,,1,,2^,,}1,,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+C(C(Ω₂+σ⁺,σ),σ),0),0),0)
{1,,1{1,,3{1,,`1`,,1,,2^,,}1,,2}2{1,,`1`,,1,,2^,,}1,,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+C(C(Ω₂+σ⁺⁺,σ),σ),0),0),0)
{1,,1{1,,3{1,,`1`,,1,,2^,,}1,,2}1{1,,2{1,,`1`,,1,,2^,,}1,,2}2{1,,`1`,,1,,2^,,}1,,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+C(C(Ω₂2,σ),σ),0),0),0)
{1,,1{1,,3{1,,`1`,,1,,2^,,}1,,2}1{1,,2{1,,`1`,,1,,2^,,}1,,2}1,2{1,,`1`,,1,,2^,,}1,,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+C(C(Ω₂2+1,0),σ),0),0),0)
{1,,1{1,,3{1,,`1`,,1,,2^,,}1,,2}1{1,,2{1,,`1`,,1,,2^,,}1,,2}1{1{1,,`1`,,1,,2^,,}1,,2}2{1,,`1`,,1,,2^,,}1,,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+σ⁺,0),0),0)
{1{1,,`1`,,1,,2^,,}1,,1,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+σ⁺+1,0),0),0)
{1{1,,`1`,,1,,2^,,}1{1,,`1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+C(C(Ω₂+σ,σ),σ⁺),0),0),0)
{1{1,,`1`,,1,,2^,,}1{1,,`1,,1,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+C(C(Ω₂+σ⁺+1,σ),σ⁺),0),0),0)
{1{1,,`1`,,1,,2^,,}1{1,,`1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+C(C(Ω₂+σ⁺⁺,σ),σ⁺),0),0),0)
{1{1,,`1`,,1,,2^,,}1{1,,`1`,,1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+C(C(Ω₂+σ⁺⁺+σ,σ),σ⁺),0),0),0) (here Taranovsky’s ordinal notation has an unexpected growth boost because C(Ω₂+σ⁺⁺+C(C(Ω₂+σ⁺⁺,σ),σ⁺),0) is valid)
{1,,`1`,,1,,1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+C(C(Ω₂+σ⁺⁺+σ⁺+1,σ),σ⁺),0),0),0)
{1,,`1`,,1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1,,`1`,,1`,,1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺+C(C(Ω₂2+1,0),σ⁺),0),0),0)
{1,,`1`,,1`,,1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺2,0),0),0)
{1{1,,`1`,,1`,,1,,2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺2+1,0),0),0)
{1{1,,`1`,,1`,,1,,2^,,}1{1,,`1,,1,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺2+C(C(Ω₂+σ⁺+1,σ),σ⁺),0),0),0)
{1{1,,`1`,,1`,,1,,2^,,}1{1,,`1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺2+C(C(Ω₂+σ⁺⁺,σ),σ⁺),0),0),0)
{1{1,,`1`,,1`,,1,,2^,,}1{1,,`1`,,1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺2+C(C(Ω₂+σ⁺⁺2,σ),σ⁺),0),0),0)
{1{1,,`1`,,1`,,1,,2^,,}1{1,,`1`,,1`,,1,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺2+C(C(Ω₂+σ⁺⁺2+σ,σ),σ⁺),0),0),0)
{1,,`1`,,1`,,1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺2+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1,,`1`,,1`,,1`,,1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺3,0),0),0)
{1,,`1`,,1`,,1`,,1`,,1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺4,0),0),0)
{1,,`1{2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+1),0),0),0)
{1,,`1{1,,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+σ),0),0),0)
{1{1,,`1{1{1{1,,`1{1,,2^`,,}2^,,}2}2^`,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+σ)+1,0),0),0)
{1{1,,`1{1,,2^`,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+σ⁺)+1,0),0),0)
{1{1,,`1{1,,2^`,,}2^,,}1,,1,2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+σ⁺)+σ⁺+1,0),0),0)
{1{1,,`1{1,,2^`,,}2^,,}1{1,,`1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+σ⁺)+C(C(Ω₂+σ⁺⁺,σ),σ⁺),0),0),0)
{1{1,,`1{1,,2^`,,}2^,,}1{1,,`1{1,,2^`,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+σ⁺)+C(C(Ω₂+ω^(σ⁺⁺+σ),σ),σ⁺),0),0),0)
{1,,`1{1,,2^`,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+σ⁺)+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1,,`1{1,,2^`,,}1`,,1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+σ⁺)+σ⁺⁺,0),0),0)
{1,,`1{2,,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+σ⁺+1),0),0),0)
{1,,`1{1,,3^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+σ⁺+σ),0),0),0)
{1,,`1{1{1{1,,`1`,,2^,,}2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂+σ⁺⁺,σ),σ⁺)),0),0),0)
{1,,`1{1{1{1,,`1{2,,2^`,,}2^,,}2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂+ω^(σ⁺⁺+σ⁺+1),σ),σ⁺)),0),0),0)
{1,,`1{1`,,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1{1`,,2^`,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+1,0),0),0)
{1{1,,`1{1`,,2^`,,}2^,,}1{1,,`1{2^`,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂+ω^(σ⁺⁺+1),σ),σ⁺),0),0),0)
{1{1,,`1{1`,,2^`,,}2^,,}1{1,,`1{1{1{1,,`1{2^`,,}2^,,}2^,,}2^`,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂+ω^(σ⁺⁺+1),σ),σ⁺)),σ),σ⁺),0),0),0)
{1{1,,`1{1`,,2^`,,}2^,,}1{1,,`1{1`,,2^`,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂2,σ),σ⁺),0),0),0) (here an erratic thing comes because C(C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺)),σ),σ⁺) is not valid)
{1{2{1,,`1{1`,,2^`,,}2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+ω^(C(C(Ω₂2,σ),σ⁺)+1),0),0),0)
{1`,,2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(σ⁺⁺,C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1{2^`,,}2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂+ω^(σ⁺⁺+1),σ),C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1{1{1{1,,`1{2^`,,}2^,,}2^,,}2^`,,}2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂+ω^(σ⁺⁺+1),σ),σ⁺)),σ),C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺)),σ),C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1,2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+1,σ),C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1{1{1,,`1{2^`,,}2^,,}2^,,}2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂+ω^(σ⁺⁺+1),σ),σ⁺),σ),C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂2,σ),σ⁺),σ),C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1{2{1,,`1{1`,,2^`,,}2^,,}2^,,}2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+ω^(C(C(Ω₂2,σ),σ⁺)+1),σ),C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1`,,2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂2,σ),C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1`,,2^,,}1,2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂2,σ)+1,σ⁺),0),0),0)
{1{1{1,,`1,2^,,}2,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1`,,2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂2,σ)+C(Ω₂+1,σ),σ⁺),0),0),0)
{1{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}2^,,}2,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1`,,2^,,} 2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂2,σ)+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺)),σ),σ⁺),0),0),0)
{1{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1`,,2^,,}2,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1`,,2^,,} 2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂2,σ)2,σ⁺),0),0),0)
{1{1,,`2{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1`,,2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂2,σ)⁺,σ⁺),0),0),0)
{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}2`,,2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺)),C(Ω₂2,σ)),σ⁺),0),0),0)
{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1`,,3^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂2,C(Ω₂2,σ)),σ⁺),0),0),0)
{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1`,,1,2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+C(C(Ω₂2+1,0),σ⁺),0),0),0)
{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1`,,1,,2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+σ⁺⁺,0),0),0)
{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1{2^`,,}2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))+ω^(σ⁺⁺+1),0),0),0)
{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺))2,0),0),0)
{1{1,,`1{2{1{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺)+1),0),0),0)
{1{1,,`1{1{1{1,,`1{1`,,2^`,,}2^,,}2^,,}3^`,,}2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),σ⁺)2),0),0),0)
{1{1,,`1{1{1{1,,`1{2^`,,}2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,}2^`,,}2^,,}2{1,,`1{1`,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂+ω^(σ⁺⁺+1),σ),C(C(Ω₂2,σ),σ⁺))),0),0),0)
{1{1,,`1{1`,,2^`,,}2^,,}3^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ),C(C(Ω₂2,σ),σ⁺))),0),0),0) (now it returns to the normal)
{1{1,,`1{1`,,2^`,,}2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ)+1,σ⁺)),0),0),0)
{1,,`2{1`,,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2,σ)⁺,σ⁺)),0),0),0)
{1,,`1{1`,,2^`,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺+C(C(Ω₂2+1,0),σ⁺)),0),0),0)
{1,,`1{1`,,2^`,,}1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺2),0),0),0)
{1,,`1{1`,,2^`,,}1{2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺2)+ω^(σ⁺⁺+1),0),0),0)
{1,,`1{1`,,2^`,,}1{1`,,2^`,,}1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺2)2,0),0),0)
{1,,`1{2`,,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺2+1),0),0),0)
{1,,`1{1`,,1,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^ω^(σ⁺⁺+1),0),0),0)
{1,,`1{1` `,,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺⁺,σ⁺⁺),0),0),0)
{1,,`1{1{1,,`1,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+1,σ),σ⁺⁺),0),0),0)
{1,,`1{1{1,,`1,,1,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺+1,σ),σ⁺⁺),0),0),0)
{1,,`1{1{1,,`1{1{1,,`1,2^,,}2^,,}2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+1,σ),σ⁺),σ),σ⁺⁺),0),0),0)
{1,,`1{1{1,,`1{1{1,,`1`,,2^,,}2^,,}2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+σ⁺⁺,σ),σ⁺),σ),σ⁺⁺),0),0),0)
{1,,`1{1{1,,`1{1{1,,`1{1{1,,`1,2^,,}2^`,,}2^,,}2^,,}2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+C(C(Ω₂+1,σ),σ⁺⁺),σ),σ⁺),σ),σ⁺⁺),0),0),0)
{1,,`1{1{1,,`1`,,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂2,σ),σ⁺),σ),σ⁺⁺),0),0),0)
{1,,`2{1{1,,`1`,,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂2,σ)⁺,σ⁺),σ),σ⁺⁺),0),0),0)
{1,,`1{1{1,,`1`,,2^,,}2^`,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂2+1,0),σ⁺),σ),σ⁺⁺),0),0),0)
{1,,`1{1{1,,`1`,,2^,,}2^`,,}1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺⁺,σ),σ⁺⁺),0),0),0)
{1,,`1{2{1,,`1`,,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(C(C(Ω₂+σ⁺⁺,σ),σ⁺⁺)+1),0),0),0)
{1,,`1{1{1,,`1`,,2^,,}1,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺⁺,σ)+1,σ⁺⁺),0),0),0)
{1,,`1{1{1,,`2`,,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺⁺,σ)⁺,σ⁺⁺),0),0),0)
{1,,`1{1{1,,`1`,,1,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺⁺+1,σ),σ⁺⁺),0),0),0)
{1,,`1{1{1,,`1{1{1,,`1,2^,,}2^`,,}2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+1,σ),σ⁺⁺),σ),σ⁺⁺),0),0),0)
{1,,`1{1{1,,`1{1{1,,`1`,,2^,,}2^`,,}2^,,}2^`,,}1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+σ⁺⁺,σ),σ⁺⁺),σ),σ⁺⁺),0),0),0)
{1,,`1` `,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺),0),0),0)
{1{1,,`1` `,,2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+1,0),0),0)
{1{1,,`1` `,,2^,,}1{1,,`1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂+σ⁺⁺,σ),σ⁺),0),0),0)
{1{1,,`1` `,,2^,,}1{1,,`1{1{1,,`1`,,2^,,}2^`,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂+C(C(Ω₂+σ⁺⁺,σ),σ⁺⁺),σ),σ⁺),0),0),0)
{1{1,,`1` `,,2^,,}1{1,,`1` `,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂2,σ),σ⁺),0),0),0) (here’s another similar yet erratic thing)
{1{1,,`1`,,2^,,}2{1,,`1` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂+σ⁺⁺,σ),C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1` `,,2^,,}3^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂2,σ),C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1` `,,2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂2,σ)+1,σ⁺),0),0),0)
{1,,`2` `,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂2,σ)⁺,σ⁺),0),0),0)
{1,,`1`,,2` `,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂+σ⁺⁺,C(Ω₂2,σ)),σ⁺),0),0),0)
{1,,`1{1{1,,`1` `,,2^,,}2^`,,}2` `,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂2,C(Ω₂2,σ)),σ⁺),0),0),0)
{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,2` `,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂2+1,0),σ⁺),0),0),0)
{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+σ⁺⁺,0),0),0)
{1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+σ⁺⁺+1,0),0),0)
{1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}1{1,,`1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+σ⁺⁺+C(C(Ω₂+σ⁺⁺,σ),σ⁺),0),0),0)
{1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}1{1,,`1` `,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+σ⁺⁺+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,2` `,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+σ⁺⁺+C(C(Ω₂2+1,0),σ⁺),0),0),0)
{1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+σ⁺⁺2,0),0),0)
{1{2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+ω^(σ⁺⁺+1),0),0),0)
{1{1,,`1,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂+1,σ),σ⁺⁺),0),0),0)
{1{1,,`1{1{1,,`1` `,,2^,,}2^,,}2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂+C(C(Ω₂2,σ),σ⁺),σ),σ⁺⁺),0),0),0)
{1{1,,`1{1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,2` `,,2^,,}2^,,}2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂+C(C(Ω₂2+1,0),σ⁺),σ),σ⁺⁺),0),0),0)
{1{1,,`1{1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂+σ⁺⁺,σ),σ⁺⁺),0),0),0)
{1{1,,`2{1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂+σ⁺⁺,σ)⁺,σ⁺⁺),0),0),0)
{1{1,,`1{1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}1,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂+σ⁺⁺+1,σ),σ⁺⁺),0),0),0)
{1{1,,`1{1{1,,`1,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂+C(C(Ω₂+1,σ),σ⁺⁺),σ),σ⁺⁺),0),0),0)
{1{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)2,0),0),0)
{1{1{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)2+1,0),0),0)
{1{1{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}1{1{1,,`1` `,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)2+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1{1{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}1{1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)2+σ⁺⁺,0),0),0)
{1{1{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}1{1{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺)3,0),0),0)
{1{2{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(C(C(Ω₂2,σ),σ⁺⁺)+1),0),0),0)
{1{1,,`1,2^,,}2{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+1,σ),C(C(Ω₂2,σ),σ⁺⁺)),0),0),0)
{1{1,,`1{1{1,,`1` `,,2^,,}2^,,}2^,,}2{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂2,σ),σ⁺),σ),C(C(Ω₂2,σ),σ⁺⁺)),0),0),0)
{1{1,,`1{1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2^,,}2{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺⁺,σ),C(C(Ω₂2,σ),σ⁺⁺)),0),0),0)
{1{1,,`1{1{1,,`1,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2^,,}2{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+1,σ),σ⁺⁺),σ),C(C(Ω₂2,σ),σ⁺⁺)),0),0),0)
{1{1,,`1{1{1,,`1{1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2^,,}2{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+σ⁺⁺,σ),σ⁺⁺),σ),C(C(Ω₂2,σ),σ⁺⁺)),0),0),0)
{1{1,,`1{1{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2^,,}2{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺),σ),C(C(Ω₂2,σ),σ⁺⁺)),0),0),0)
{1{1,,`1{1{1,,`1,2^,,}2{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2^,,}2{1,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+1,σ),C(C(Ω₂2,σ),σ⁺⁺)),σ),C(C(Ω₂2,σ),σ⁺⁺)),0),0),0)
{1{1,,`1`,,2^,,}3{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),C(C(Ω₂2,σ),σ⁺⁺)),0),0),0)
{1{1,,`1`,,2^,,}1,2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ)+1,σ⁺⁺),0),0),0)
{1{1{1,,`1,2^,,}2,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ)+C(Ω₂+1,σ),σ⁺⁺),0),0),0)
{1{1{1,,`1{1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2^,,}2,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ)+C(Ω₂+σ⁺⁺,σ),σ⁺⁺),0),0),0)
{1{1{1,,`1`,,2^,,}2,,`1`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ)2,σ⁺⁺),0),0),0)
{1{1,,`2`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ)⁺,σ⁺⁺),0),0),0)
{1{1,,`1{1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2`,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺⁺,C(Ω₂2,σ)),σ⁺⁺),0),0),0)
{1{1,,`1`,,3^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,C(Ω₂2,σ)),σ⁺⁺),0),0),0)
{1{1,,`1`,,1,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+1,0),σ⁺⁺),0),0),0)
{1{1,,`1`,,1{1{1{1,,`1`,,1,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2}2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+1,0),σ⁺⁺),0),0),σ⁺⁺),0),0),0)
{1{1,,`1`,,1,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),0)

Up to here, it seems that C(Ω₂,C(Ω₂2,0)) corresponds to the double comma, and C(Ω₂,C(Ω₂,C(Ω₂2,0))) corresponds to {1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}.

Up to a C(Ω₂+C(Ω₂2,0),C(Ω₂2,0))

Now let separator ■ = {1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,} and separator ♦ = {1{1{1,,`1`,,1,,2^,,}2■2^,,}2} = {1{1{1,,`1`,,1,,2^,,}2{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,,2` `,,2^,,}2^,,}2} and let ordinal σ = C(Ω₂2,0). And α⁺ is shorthand for C(Ω₂,α).

{1{1{1,,`1`,,1♦2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),0)
{1{1,,1,,1,2}2{1{1,,`1`,,1♦2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+σ⁺+1,0),0),0)
{1{1{1,,`1`,,1{1{1,,`1`,,1,,2^,,}2}2^,,}2}2{1{1,,`1`,,1♦2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,0),0),σ⁺),0),0),0)
{1{1{1,,`1`,,1{1{1{1,,`1`,,1♦2^,,}2■2^,,}2}2^,,}2}2{1{1,,`1`,,1♦2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺),0),0),0)
{1{1{1,,`1`,,1,,2^,,}2}2{1{1,,`1`,,1♦2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+σ⁺⁺,0),0),0)
{1{1{1,,`1` `,,2^,,}2}2{1{1,,`1`,,1♦2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺),0),0),0)
{1{1{1{1,,`1`,,1♦2^,,}2■2^,,}2}2{1{1,,`1`,,1♦2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺),0),0),0)
{1,,1,,2{1{1,,`1`,,1♦2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(σ,C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺),0)),0),0)
{1,,1,,1,2{1{1,,`1`,,1♦2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺+1,C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺),0)),0),σ),C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺),0)),0),0)
{1{1,,`1`,,1,,2^,,}2{1{1,,`1`,,1♦2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺,C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺),0)),0),σ),C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺),0)),0),0)
{1{1{1,,`1`,,1♦2^,,}2■2^,,}3} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ),C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺),0)),0),0)
{1{1{1{1,,`1`,,1♦2^,,}2■2^,,}3}2{1{1,,`1`,,1♦2^,,}2■2^,,}3} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺),C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺),0)),0),0)
{1{1{1,,`1`,,1♦2^,,}2■2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)+1,0),0),0)
{1{1{1,,`1`,,1♦2^,,}2■2^,,}1{1,,`1` `,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1{1{1,,`1`,,1♦2^,,}2■2^,,}1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1,2` `,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)+C(C(Ω₂2+1,0),σ⁺),0),0),0)
{1{1{1,,`1`,,1♦2^,,}2■2^,,}1{1,,`1{1{1,,`1` `,,2^,,}2^`,,}1{1{1{1,,`1`,,1♦2^,,}2■2^,,}2}2` `,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺),0),0),0)
{1{1{1,,`1`,,1♦2^,,}2■2^,,}1■2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)+σ⁺⁺,0),0),0)
{1{1{1,,`1`,,1♦2^,,}2■2^,,}1{1{1,,`1`,,2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)+C(C(Ω₂2,σ),σ⁺⁺),0),0),0)
{1{1{1,,`1`,,1♦2^,,}2■2^,,}1{1{1,,`1`,,2^,,}1,2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)+C(C(Ω₂2,σ)+1,σ⁺⁺),0),0),0)
{1{1{1,,`1`,,1♦2^,,}2■2^,,}1{1{1,,`1`,,3^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)+C(C(Ω₂2,C(Ω₂2,σ)),σ⁺⁺),0),0),0)
{1{1{1,,`1`,,1♦2^,,}2■2^,,}1{1{1,,`1`,,1,2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)+C(C(Ω₂2+1,0),σ⁺⁺),0),0),0)
{1{1{1,,`1`,,1♦2^,,}2■2^,,}1{1{1,,`1`,,1♦2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)2,0),0),0)
{1{2{1,,`1`,,1♦2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+ω^(C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)+1),0),0),0)
{1{1,,`1,2^,,}2{1,,`1`,,1♦2^,,}2■2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂+1,σ),C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)),0),0),0)
{1{1,,`1{1■2^,,}2^,,}2{1,,`1`,,1♦2^,,}2■2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂+σ⁺⁺,σ),C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)),0),0),0)
{1{1,,`1{1{1,,`1`,,1♦2^,,}2■2^,,}2^,,}2{1,,`1`,,1♦2^,,}2■2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺),σ),C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)),0),0),0)
{1{1,,`1`,,2^,,}2{1,,`1`,,1♦2^,,}2■2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2,σ),C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)),0),0),0)
{1{1,,`1`,,2^,,}1,2{1,,`1`,,1♦2^,,}2■2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2,σ)+1,C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)),0),0),0)
{1{1,,`2`,,2^,,}2{1,,`1`,,1♦2^,,}2■2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2,σ)⁺,C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)),0),0),0)
{1{1,,`1`,,3^,,}2{1,,`1`,,1♦2^,,}2■2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2,C(Ω₂2,σ)),C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)),0),0),0)
{1{1,,`1`,,1,2^,,}2{1,,`1`,,1♦2^,,}2■2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+1,0),C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)),0),0),0)
{1{1,,`1`,,1♦2^,,}3■2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺)),0),0),0)
{1{1,,`1`,,1♦2^,,}1,2■2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0)+1,σ⁺⁺),0),0),0)
{1{1,,`2`,,1♦2^,,}2■2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0)⁺,σ⁺⁺),0),0),0)
{1{1,,`1`,,1♦1,2^,,}2■2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)+1,0),σ⁺⁺),0),0),0)
{1{1,,`1`,,1♦1♦2^,,}2■2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0)2,0),0)
{1{1,,`1`,,1,,2^,,}2{1{1,,`1`,,1,,2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺,C(Ω₂+σ⁺⁺⁺,0)),0),0)
{1{1{1,,`1`,,1{1{1{1,,`1`,,1♦2^,,}2■2^,,}2}2^,,}2■2^,,}2{1{1,,`1`,,1,,2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺),0),0),σ⁺⁺),C(Ω₂+σ⁺⁺⁺,0)),0),0)
{1{1{1,,`1`,,1♦2^,,}2■2^,,}2{1{1,,`1`,,1,,2^,,}2■2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,0),0),σ⁺⁺),C(Ω₂+σ⁺⁺⁺,0)),0),0)
{1{1{1,,`1`,,1,,2^,,}2■2^,,}3} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺,C(Ω₂+σ⁺⁺⁺,0)),0),0)
{1{1{1,,`1`,,1,,2^,,}2■2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+1,0),0),0)
{1{1{1,,`1`,,1,,2^,,}2■2^,,}1{1,,`1,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+1,σ),σ⁺),0),0),0)
{1{1{1,,`1`,,1,,2^,,}2■2^,,}1{1,,`1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺,σ),σ⁺),0),0),0)
{1{1{1,,`1`,,1,,2^,,}2■2^,,}1{1,,`1` `,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺,σ),σ⁺),0),0),0)
{1{1{1,,`1`,,1,,2^,,}2■2^,,}1{1,,`2` `,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺,σ)⁺,σ⁺),0),0),0)
{1,,`1` `,,3^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺,C(Ω₂+σ⁺⁺⁺,σ)),σ⁺),0),0),0) (the growth boost appears again)
{1,,`1` `,,1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺+1,σ),σ⁺),0),0),0)
{1,,`1` `,,1{1{1,,`1` `,,2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺,σ),σ⁺),σ),σ⁺),0),0),0)
{1,,`1` `,,1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1{1,,`1` `,,2^,,}2{1,,`1` `,,1`,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺,σ),C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1` `,,1{1{1,,`1` `,,1`,,2^,,}2^,,}2^,,}2{1,,`1` `,,1`,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺+C(C(Ω₂2,σ),σ⁺),σ),C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1` `,,1`,,2^,,}3^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂2,σ),C(C(Ω₂2,σ),σ⁺)),0),0),0)
{1{1,,`1` `,,1`,,2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂2,σ)+1,σ⁺),0),0),0)
{1{1,,`1` `,,1`,,2^,,}2,,`1` `,,1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂2,σ)2,σ⁺),0),0),0)
{1,,`2` `,,1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂2,σ)⁺,σ⁺),0),0),0)
{1,,`1` `,,1`,,3^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂2,C(Ω₂2,σ)),σ⁺),0),0),0)
{1,,`1` `,,1`,,1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂2+1,0),σ⁺),0),0),0)
{1,,`1` `,,1`,,1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+σ⁺⁺,0),0),0)
{1,,`1` `,,1`,,1`,,1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+σ⁺⁺2,0),0),0)
{1,,`1` `,,1{2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+ω^(σ⁺⁺+1),0),0),0)
{1,,`1` `,,1{1{1,,`1,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+1,σ),σ⁺⁺),0),0),0)
{1,,`1` `,,1{1{1,,`1{1{1,,`1` `,,2^,,}2^,,}2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+C(C(Ω₂+σ⁺⁺⁺,σ),σ⁺),σ),σ⁺⁺),0),0),0)
{1,,`1` `,,1{1{1,,`1{1{1,,`1` `,,1`,,1,,2^,,}2^,,}2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+C(C(Ω₂+σ⁺⁺⁺+σ⁺⁺,σ),σ⁺),σ),σ⁺⁺),0),0),0)
{1,,`1` `,,1{1{1,,`1`,,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+C(C(Ω₂2,σ),σ⁺),σ),σ⁺⁺),0),0),0)
{1{1,,`1` `,,1{1{1,,`1`,,2^,,}2^`,,}2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+C(C(Ω₂2,σ)+1,σ⁺),σ),σ⁺⁺),0),0),0)
{1,,`2` `,,1{1{1,,`1`,,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+C(C(Ω₂2,σ)⁺,σ⁺),σ),σ⁺⁺),0),0),0)
{1,,`1` `,,1{1{1,,`1`,,2^,,}2^`,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+C(C(Ω₂2+1,0),σ⁺),σ),σ⁺⁺),0),0),0)
{1,,`1` `,,1{1{1,,`1`,,2^,,}2^`,,}1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺,σ),σ⁺⁺),0),0),0)
{1{1,,`1` `,,1{1{1,,`1`,,2^,,}2^`,,}1,,2^,,}1{1,,`1` `,,1{1{1,,`1`,,2^,,}2^`,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺,σ),σ⁺⁺)+C(C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺,σ),σ⁺⁺),σ),σ⁺),0),0),0)
{1,,`1` `,,1{1{1,,`1`,,2^,,}2^`,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺,σ),σ⁺⁺)+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1,,`1` `,,1{1{1,,`1`,,2^,,}2^`,,}1`,,1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺,σ),σ⁺⁺)+σ⁺⁺,0),0),0)
{1,,`1` `,,1{2{1,,`1`,,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+ω^(C(C(Ω₂+σ⁺⁺,σ),σ⁺⁺)+1),0),0),0)
{1,,`1` `,,1{1{1,,`1`,,2^,,}1,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺,σ)+1,σ⁺⁺),0),0),0)
{1,,`1` `,,1{1{1,,`2`,,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺,σ)⁺,σ⁺⁺),0),0),0)
{1,,`1` `,,1{1{1,,`1`,,1,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺+1,σ),σ⁺⁺),0),0),0)
{1,,`1` `,,1{1{1,,`1{1{1,,`1`,,1,2^,,}2^`,,}2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+C(C(Ω₂+σ⁺⁺+1,σ),σ⁺⁺),σ),σ⁺⁺),0),0),0)
{1,,`1` `,,1{1{1,,`1` `,,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺,σ),σ⁺⁺),0),0),0)
{1,,`1` `,,1{1{1,,`1` `,,2^,,}2^`,,}1`,,1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺,σ),σ⁺⁺)+σ⁺⁺,0),0),0)
{1,,`1` `,,1{1{1,,`1` `,,2^,,}1,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺,σ)+1,σ⁺⁺),0),0),0)
{1,,`1` `,,1{1{1,,`2` `,,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺,σ)⁺,σ⁺⁺),0),0),0)
{1,,`1` `,,1{1{1,,`1` `,,1,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺+1,σ),σ⁺⁺),0),0),0)
{1,,`1` `,,1{1{1,,`1` `,,1{1{1,,`1` `,,1,2^,,}2^`,,}2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺+C(C(Ω₂+σ⁺⁺⁺+1,σ),σ⁺⁺),σ),σ⁺⁺),0),0),0)
{1,,`1` `,,1` `,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂2,σ),σ⁺⁺),0),0),0)
{1{1,,`1` `,,1` `,,2^,,}1{1,,`1` `,,1` `,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺⁺⁺+C(C(Ω₂2,σ),σ⁺⁺)+C(C(Ω₂2,σ),σ⁺),0),0),0) (erratic thing again)

Despite of the erratic thing, which contributes little to the strength of TON (vs. sDAN), the C(Ω₂,C(Ω₂,C(Ω₂,C(Ω₂2,0)))) approximately corresponds to {1,,`3^,,} (or the ` `,,), then approximately

{1,,`1{2^{` `,,}}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺⁺+1),0),0),0)
{1,,`1{1` `,,2^{` `,,}}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ⁺⁺⁺+C(C(Ω₂2,σ),σ⁺⁺)),0),0),0)
{1,,`1{1` `,,1,2^{` `,,}}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^ω^(σ⁺⁺⁺+1),0),0),0)
{1,,`1{1{2^{` `,,}}2^{` `,,}}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^ω^ω^(σ⁺⁺⁺+1),0),0),0)
{1,,`1{1` ` `,,2^{` `,,}}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ⁺⁺⁺⁺,σ⁺⁺⁺),0),0),0)
{1,,`1{1{1,,`1,2^,,}2^{` `,,}}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+1,σ),σ⁺⁺⁺),0),0),0)
{1,,`1{1{1,,`1,,2^,,}2^{` `,,}}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ,σ),σ⁺⁺⁺),0),0),0)
{1,,`1{1{1,,`1{2^,,}2^,,}2^{` `,,}}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+ω^(σ⁺+1),σ),σ⁺⁺⁺),0),0),0)
{1,,`1{1{1,,`1{2^`,,}2^,,}2^{` `,,}}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+ω^(σ⁺⁺+1),σ),σ⁺⁺⁺),0),0),0)
{1,,`1{1{1,,`1{2^{` `,,}}2^,,}2^{` `,,}}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+ω^(σ⁺⁺⁺+1),σ),σ⁺⁺⁺),0),0),0)
{1,,`1` ` `,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺⁺),0),0),0)

As shown above, the recursion level of {1,,`1`,,2^,,} is C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,C(Ω₂2,0)),C(Ω₂,C(Ω₂2,0))),0),0),0), the recursion level of {1,,`1` `,,2^,,} is C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,C(Ω₂2,0)),C(Ω₂,C(Ω₂,C(Ω₂2,0)))),0),0),0), the recursion level of {1,,`1` ` `,,2^,,} is C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,C(Ω₂2,0)),C(Ω₂,C(Ω₂,C(Ω₂,C(Ω₂2,0))))),0),0),0), and so on. Generally, the recursion level of {1,,`1{1,,`k^,,}2^,,} (k > 1) is between C(C(Ω₂2+C(Ω₂+C(Ω₂,C(Ω₂,…C(Ω₂,C(Ω₂2,0))…)),0),0),0) (with k-1 Ω₂′s in the blue part) and C(C(Ω₂2+C(Ω₂+C(Ω₂,C(Ω₂,…C(Ω₂,C(Ω₂2,0))…)),0),0),0) (with k Ω₂′s in the blue part), so {1,,`1{1,,`1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,C(Ω₂2,0)),0),0),0).

Now let ordinal σ = C(Ω₂2,0). And α⁺ is shorthand for C(Ω₂,α).

{1{1,,`1{1,,`1,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ),0),0),0)
{1{1,,1,,1,2}2{1,,`1{1,,`1,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ),0)+C(Ω₂+σ⁺+1,0),0),0)
{1{1{1,,`1`,,2^,,}2}2{1,,`1{1,,`1,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ),0)+C(Ω₂+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1{1{1,,`1` `,,2^,,}2}2{1,,`1{1,,`1,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ),0)+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺),0),0),0)
{1{1{1,,`1{1,,`1,2^,,}2^,,}2}2{1,,`1{1,,`1,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ),0)2,0),0)
{1,,1,,1,2{1,,`1{1,,`1,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺+1,C(Ω₂+C(Ω₂+1,σ),0)),0),0)
{1{1,,`1`,,2^,,}2{1,,`1{1,,`1,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺),C(Ω₂+C(Ω₂+1,σ),0)),0),0)
{1{1,,`1` `,,2^,,}2{1,,`1{1,,`1,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺),C(Ω₂+C(Ω₂+1,σ),0)),0),0)
{1{1,,`1{1,,`1,2^,,}2^,,}3} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ),C(Ω₂+C(Ω₂+1,σ),0)),0),0)
{1{1,,`1{1,,`1,2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+1,0),0),0)
{1{1,,`1{1,,`1,2^,,}2^,,}1{1,,`1,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂+1,σ),σ⁺),0),0),0)
{1{1,,`1{1,,`1,2^,,}2^,,}1{1,,`1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂+σ⁺⁺,σ),σ⁺),0),0),0)
{1{1,,`1{1,,`1,2^,,}2^,,}1{1,,`1` `,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂+σ⁺⁺⁺,σ),σ⁺),0),0),0)
{1{1,,`1{1,,`1,2^,,}2^,,}1{1,,`1{1,,`1,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂+C(Ω₂+1,σ),σ),σ⁺),0),0),0)
{1{1,,`1,2^,,}1{1,,`1{1,,`1,2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂+1,σ),C(C(Ω₂+C(Ω₂+1,σ),σ),σ⁺)),0),0),0)
{1{1,,`1{1,,`1,2^,,}2^,,}3^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂+C(Ω₂+1,σ),σ),C(C(Ω₂+C(Ω₂+1,σ),σ),σ⁺)),0),0),0)
{1{1,,`1{1,,`1,2^,,}2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂+C(Ω₂+1,σ),σ)+1,σ⁺),0),0),0)
{1,,`2{1,,`1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂+C(Ω₂+1,σ),σ)⁺,σ⁺),0),0),0)
{1,,`1{1,,`1,2^,,}3^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂+C(Ω₂+1,σ),C(Ω₂+C(Ω₂+1,σ),σ)),σ⁺),0),0),0)
{1,,`1{1,,`1,2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂+C(Ω₂+1,σ)+1,σ),σ⁺),0),0),0)
{1,,`1{1,,`1,2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1,,`2{1,,`1,2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂2,σ)⁺,σ⁺),0),0),0)
{1,,`1{1,,`1,2^,,}1`,,1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂2+1,0),σ⁺),0),0),0)
{1,,`1{1,,`1,2^,,}1`,,1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+σ⁺⁺,0),0),0)
{1,,`1{1,,`1,2^,,}1{2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+ω^(σ⁺⁺+1),0),0),0)
{1,,`1{1,,`1,2^,,}1{1{1,,`1,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂+1,σ),σ⁺⁺),0),0),0)
{1,,`1{1,,`1,2^,,}1{1{1,,`1{1,,`1,2^,,}2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂+C(Ω₂+1,σ),σ),σ⁺⁺),0),0),0)
{1,,`1{1,,`1,2^,,}1` `,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂2,σ),σ⁺⁺),0),0),0)
{1,,`1{1,,`1,2^,,}1{2^{` `,,}}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+σ⁺⁺⁺,0),0),0)
{1,,`1{1,,`1,2^,,}1` ` `,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)+C(C(Ω₂2,σ),σ⁺⁺⁺),0),0),0)
{1,,`1{1,,`1,2^,,}1{1,,`1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ)2,0),0),0)
{1,,`1{1{1,,`2,2^,,}2,,`1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+1,σ)⁺,C(Ω₂+1,σ)),0),0),0)
{1,,`1{1{1,,`1{1,,`1,2^,,}2^,,}2,,`1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(Ω₂+1,σ),σ),C(Ω₂+1,σ)),0),0),0)
{1,,`1{1{1,,`1{1{1,,`1{1,,`1,2^,,}2^,,}2,,`1,2^,,}2^,,}2,,`1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+C(Ω₂+1,σ),σ),C(Ω₂+1,σ)),σ),C(Ω₂+1,σ)),0),0),0)
{1,,`1{1,,`2,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),C(Ω₂+1,σ)),0),0),0)
{1,,`1{1,,`3,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),C(Ω₂+1,σ)⁺),0),0),0)
{1,,`1{1,,`1,3^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,C(Ω₂+1,σ)),0),0),0)
{1,,`1{1,,`1,1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+2,σ),0),0),0)
{1,,`1{1,,`1{1{1,,`1{1,,`1,2^,,}2^,,}2}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂+C(Ω₂+1,σ),0),σ),0),0),0)
{1,,`1{1,,`1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ),0),0),0)

Due to the “growth boosts”, {1,,`k^,,} approximately corresponds to C(Ω₂,C(Ω₂,…C(Ω₂,C(Ω₂2,0))…)) (with k Ω₂′s in the blue part), and {1,,`1,2^,,} approximately corresponds to C(Ω₂+1,C(Ω₂2,0)).

Beyond C(Ω₂+C(Ω₂2,0),C(Ω₂2,0))

Now let separator ♦ = {1{1,,`1{1,,`1,,2^,,}2^,,}2} and let ordinal σ = C(Ω₂2,0). And α⁺ is shorthand for C(Ω₂,α).

{1{1,,`1{1,,`1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ),0),0),0)
{1{1,,1,,1,2}2{1,,`1{1,,`1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ),0)+C(Ω₂+σ⁺+1,0),0),0)
{1{1{1,,`1`,,2^,,}2}2{1,,`1{1,,`1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ),0)+C(Ω₂+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1{1{1,,`1{1,,`1,2^,,}2^,,}2}2{1,,`1{1,,`1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ),0)+C(Ω₂+C(Ω₂+1,σ),0),0),0)
{1{1{1,,`1{1,,`1♦2^,,}2^,,}2}2{1,,`1{1,,`1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ),0)2,0),0)
{1,,1,,1,2{1,,`1{1,,`1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺+1,C(Ω₂+C(Ω₂+σ,σ),0)),0),0)
{1{1,,`1{1,,`1,2^,,}2^,,}2{1,,`1{1,,`1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ),C(Ω₂+C(Ω₂+σ,σ),0)),0),0)
{1{1,,`1{1,,`1{1{1,,`1{1,,`1♦2^,,}2^,,}2}2^,,}2^,,}2{1,,`1{1,,`1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂+C(Ω₂+σ,σ),0),σ),C(Ω₂+C(Ω₂+σ,σ),0)),0),0)
{1{1,,`1{1,,`1♦2^,,}2^,,}3} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ),C(Ω₂+C(Ω₂+σ,σ),0)),0),0)
{1{1,,`1{1,,`1♦2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ)+1,0),0),0)
{1{1,,`1{1,,`1♦2^,,}2^,,}1{1,,`1{1,,`1,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ)+C(C(Ω₂+C(Ω₂+1,σ),σ),σ⁺),0),0),0)
{1{1,,`1{1,,`1♦2^,,}2^,,}1{1,,`1{1,,`1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ)+C(C(Ω₂+C(Ω₂+σ,σ),σ),σ⁺),0),0),0)
{1{1,,`1{1,,`1♦2^,,}2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ)+C(C(Ω₂+C(Ω₂+σ,σ),σ)+1,σ⁺),0),0),0)
{1,,`2{1,,`1♦2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ)+C(C(Ω₂+C(Ω₂+σ,σ),σ)⁺,σ⁺),0),0),0)
{1,,`1{1,,`1♦2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ)+C(C(Ω₂+C(Ω₂+σ,σ)+1,σ),σ⁺),0),0),0)
{1,,`1{1,,`1♦2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ)+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1,,`1{1,,`1♦2^,,}1`,,1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ)+σ⁺⁺,0),0),0)
{1,,`1{1,,`1♦2^,,}1` `,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ)+C(C(Ω₂2,σ),σ⁺⁺),0),0),0)
{1,,`1{1,,`1♦2^,,}1{1,,`1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ)+C(Ω₂+1,σ),0),0),0)
{1,,`1{1,,`1♦2^,,}1{1,,`1♦2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,σ)2,0),0),0)
{1,,`1{1{1,,`1{1,,`1,2^,,}2^,,}2,,`1♦2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(Ω₂+1,σ),σ),C(Ω₂+σ,σ)),0),0),0)
{1,,`1{1{1,,`1{1,,`1♦2^,,}2^,,}2,,`1♦2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(Ω₂+σ,σ),σ),C(Ω₂+σ,σ)),0),0),0)
{1,,`1{1,,`2♦2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),C(Ω₂+σ,σ)),0),0),0)
{1,,`1{1,,`1,2♦2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,C(Ω₂+σ,σ)),0),0),0)
{1,,`1{1,,`1♦3^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,C(Ω₂+σ,σ)),0),0),0)
{1,,`1{1,,`1♦1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ+1,σ),0),0),0)
{1,,`1{1,,`1♦1♦2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ2,σ),0),0),0)
{1,,`1{1,,`1{2{1,,`1{1,,`1,,2^,,}2^,,}2}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+ω^(σ+1),σ),0),0),0)
{1,,2{1,,`1{1,,`1,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(σ⁺,σ),σ),0),0),0)
{1,,1,2{1,,`1{1,,`1,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂+1,σ),σ),σ),0),0),0)
{1,,1{1,,1,2{1,,`1{1,,`1,,2^,,}2^,,}2}2{1,,`1{1,,`1,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂+C(Ω₂+1,σ),σ),σ),σ),0),0),0)
{1,,1{1,,1♦2{1,,`1{1,,`1,,2^,,}2^,,}2}2{1,,`1{1,,`1,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂+C(Ω₂+σ,σ),σ),σ),σ),0),0),0)
{1,,1{1,,1{1,,2{1,,`1{1,,`1,,2^,,}2^,,}2}2{1,,`1{1,,`1,,2^,,}2^,,}2}2{1,,`1{1,,`1,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂2,σ),σ),σ),0),0),0)
{1,,2{1,,1{1,,2{1,,`1{1,,`1,,2^,,}2^,,}2}2{1,,`1{1,,`1,,2^,,}2^,,}2}2{1,,`1{1,,`1,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂2,σ)⁺,σ),σ),0),0),0)
{1,,1{1,,1{1,,2{1,,`1{1,,`1,,2^,,}2^,,}2}2{1,,`1{1,,`1,,2^,,}2^,,}2}1,2{1,,`1{1,,`1,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂2+1,0),σ),σ),0),0),0)
{1,,1{1,,1{1,,2{1,,`1{1,,`1,,2^,,}2^,,}2}2{1,,`1{1,,`1,,2^,,}2^,,}2}1♦2{1,,`1{1,,`1,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ⁺,σ),0),0),0)
{1,,1,,1,2{1,,`1{1,,`1,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ⁺+1,C(Ω₂+C(Ω₂+σ⁺,σ),0)),0),0)
{1{1,,`1{1,,`1,,2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ⁺,σ)+1,0),0),0)
{1{1,,`1{1,,`1,,2^,,}2^,,}1{1,,`1,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ⁺,σ)+C(C(Ω₂+1,σ),σ⁺),0),0),0)
{1{1,,`1{1,,`1,,2^,,}2^,,}1{1,,`1{1,,`1,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ⁺,σ)+C(C(Ω₂+C(Ω₂+σ,σ),σ),σ⁺),0),0),0)
{1{1,,`1{1,,`1,,2^,,}2^,,}1{1,,`1{1,,`1,,2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ⁺,σ)+C(C(Ω₂+C(Ω₂+σ⁺,σ),σ),σ⁺)+1,0),0),0)
{1{1,,`1{1,,`1,,2^,,}2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ⁺,σ)+C(C(Ω₂+C(Ω₂+σ⁺,σ),σ)+1,σ⁺),0),0),0)
{1,,`2{1,,`1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ⁺,σ)+C(C(Ω₂+C(Ω₂+σ⁺,σ),σ)⁺,σ⁺),0),0),0)
{1,,`1{1,,`1,,2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ⁺,σ)+C(C(Ω₂+C(Ω₂+σ⁺,σ)+1,σ),σ⁺),0),0),0)
{1,,`1{1,,`1,,2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ⁺,σ)+C(C(Ω₂2,σ),σ⁺),0),0),0)
{1,,`1{1,,`1,,2^,,}1`,,1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ⁺,σ)+σ⁺⁺,0),0),0)
{1,,`1{1,,`1,,2^,,}1{1,,`1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ⁺,σ)+C(Ω₂+1,σ),0),0),0)
{1,,`1{1,,`1,,2^,,}1{1,,`1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ⁺,σ)+C(Ω₂+σ,σ),0),0),0)
{1{1,,`1{1,,`1,,2^,,}1{1,,`1,,2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ⁺,σ)2+1,0),0),0)
{1,,`1{2,,`1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(C(Ω₂+σ⁺,σ)+1),0),0),0)
{1,,`1{1{1,,`2,,2^,,}2,,`1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ⁺,σ)⁺,C(Ω₂+σ⁺,σ)),0),0),0)
{1,,`1{1{1,,`1{1,,`1,,2^,,}2^,,}2,,`1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(Ω₂+σ,σ),σ),C(Ω₂+σ⁺,σ)),0),0),0)
{1,,`1{1,,`2,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,σ),C(Ω₂+σ⁺,σ)),0),0),0)
{1,,`1{1,,`1,2,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,C(Ω₂+σ⁺,σ)),0),0),0)
{1,,`1{1,,`1,,3^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ,C(Ω₂+σ⁺,σ)),0),0),0)
{1,,`1{1,,`1,,1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ⁺+1,σ),0),0),0)
{1,,`1{1,,`1{2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+ω^(σ⁺+1),σ),0),0),0)
{1,,`1{1,,`1{1{1,,`1{1,,`1,,2^,,}2^,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂+C(Ω₂+σ,σ),σ),σ⁺),σ),0),0),0)
{1,,`1{1,,`1{1{1,,`1{1,,`1{2^,,}2^,,}2^,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂+C(Ω₂+ω^(σ⁺+1),σ),σ),σ⁺),σ),0),0),0)
{1,,`1{1,,`1`,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂2,σ),σ⁺),σ),0),0),0)
{1,,`1{1,,`1` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂2,σ),σ⁺⁺),σ),0),0),0)
{1,,`1{1,,`1{1,,`1,2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂+1,σ),σ),0),0),0)
{1,,`1{1,,`1{1,,`1{1,,`1,2^,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂+C(Ω₂+1,σ),σ),σ),0),0),0)
{1,,`1{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,σ),0),0),0)

So {1,,`1,,`2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2,0)),0),0),0).

Up to {1,,`1{1,,`1,,`2^,,}3^,,}

Up to a C(Ω₂,C(Ω₂2,C(Ω₂2,0)))

Now let ordinal σ = σ₁ = C(Ω₂2,0), and σ_n+1 = C(Ω₂2,σ_n).

{1{1,,`1{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂,0),0),0)
{1{1,,1,,1,2}2{1,,`1{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂,0)+C(Ω₂+C(Ω₂,σ)+1,0),0),0)
{1{1{1,,`1`,,2^,,}2}2{1,,`1{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂,0)+C(Ω₂+C(σ₂,C(Ω₂,σ)),0),0),0)
{1{1{1,,`1{1,,`1,2^,,}2^,,}2}2{1,,`1{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂,0)+C(Ω₂+C(Ω₂+1,σ),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,2^,,}2^,,}2^,,}2}2{1,,`1{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂,0)+C(Ω₂+C(Ω₂+C(Ω₂+1,σ),σ),0),0),0)
{1{1{1,,`1{1,,`1,,`2^,,}2^,,}2}2{1,,`1{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂,0)2,0),0)
{1,,2{1,,`1{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(C(Ω₂,C(Ω₂+σ₂,0)),C(Ω₂+σ₂,0)),0),0)
{1,,1,,1,2{1,,`1{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ)+1,C(Ω₂+σ₂,0)),0),0)
{1{1,,`1{1,,`1,2^,,}2^,,}2{1,,`1{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ),C(Ω₂+σ₂,0)),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}3} has recursion level C(C(Ω₂2+C(Ω₂+σ₂,C(Ω₂+σ₂,0)),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+1,0),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+σ,0),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}1,,1,2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂,σ)+1,0),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}1{1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂,C(Ω₂,σ)),C(Ω₂,σ)),0),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}1{1,,`1,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂+1,σ),C(Ω₂,σ)),0),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}1{1,,`1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂+C(Ω₂,C(Ω₂,σ)),σ),C(Ω₂,σ)),0),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂+C(Ω₂+1,σ),σ),C(Ω₂,σ)),0),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(σ₂,C(Ω₂,σ)),0),0),0) (from here on, the growth slows down. C(C(Ω₂+σ₂,σ),C(Ω₂,σ)) is not valid)
{1{1,,`1,2^,,}2{1,,`1{1,,`1,,`2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂+1,σ),C(σ₂,C(Ω₂,σ))),0),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}3^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(σ₂,C(σ₂,C(Ω₂,σ))),0),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(σ₂+1,C(Ω₂,σ)),0),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}2,,`1{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(σ₂2,C(Ω₂,σ)),0),0),0)
{1,,`2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂,σ₂),C(Ω₂,σ)),0),0),0)
{1,,`1,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂+1,σ₂),C(Ω₂,σ)),0),0),0)
{1,,`1{1,,`1,2^,,}2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂+C(Ω₂+1,σ),σ₂),C(Ω₂,σ)),0),0),0)
{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(σ₃,C(Ω₂,σ)),0),0),0)
{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}3{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(σ₄,C(Ω₂,σ)),0),0),0)
{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂2+1,0),C(Ω₂,σ)),0),0),0)
{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1{1{1,,`1{1,,`1,,`2^,,}2^,,}1,2}2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂2+C(Ω₂+σ₂+1,0),0),C(Ω₂,σ)),0),0),0)
{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂,C(Ω₂,σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂,C(Ω₂,σ))+1,0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂,C(Ω₂,σ))+C(C(Ω₂+1,σ),C(Ω₂,σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂,C(Ω₂,σ))+C(σ₂,C(Ω₂,σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂,C(Ω₂,σ))2,0),0),0)
{1{1,,`1,2^,,}2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂+1,σ),C(Ω₂,C(Ω₂,σ))),0),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(σ₂,C(Ω₂,C(Ω₂,σ))),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,2{1,,`1,,`2^,,}2^,,}2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂2+1,0),C(Ω₂,C(Ω₂,σ))),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}3^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂,C(Ω₂,C(Ω₂,σ))),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}4^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂,C(Ω₂,C(Ω₂,C(Ω₂,σ)))),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+1,σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+σ,σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,,1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+C(Ω₂,σ)+1,σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1{1,,`1,2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+C(C(Ω₂+1,σ),C(Ω₂,σ)),σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1{1,,`1{1,,`1,,`2^,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+C(σ₂,C(Ω₂,σ)),σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,2{1,,`1,,`2^,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+C(C(Ω₂2+1,0),C(Ω₂,σ)),σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+C(Ω₂,C(Ω₂,σ)),σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+C(Ω₂+1,σ),σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+C(Ω₂+C(Ω₂+1,σ),σ),σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+σ₂,σ),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+σ₂,σ)+1,0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,}1 {1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+σ₂,σ)+C(Ω₂,C(Ω₂,σ)),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+σ₂,σ)2,0),0),0)
{1{2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+ω^(C(Ω₂+σ₂,σ)+1),0),0),0)
{1{1,,`1,2^,,}2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂+1,C(Ω₂+σ₂,σ)),C(Ω₂+σ₂,σ)),0),0),0)
{1{1,,`1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,}2^,,}2 {1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂+C(Ω₂+σ₂,σ),C(Ω₂+σ₂,σ)),C(Ω₂+σ₂,σ)),0),0),0)
{1{1,,`1`,,2^,,}2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂+C(Ω₂,C(Ω₂+σ₂,σ)),C(Ω₂+σ₂,σ)),C(Ω₂+σ₂,σ)),0),0),0)
{1{1,,`1{1,,`1,2^,,}2^,,}2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂+C(Ω₂+1,C(Ω₂+σ₂,σ)),C(Ω₂+σ₂,σ)),C(Ω₂+σ₂,σ)),0),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(σ₂,C(Ω₂+σ₂,σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,2{1,,`1,,`2^,,}2^,,}2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(C(Ω₂2+1,0),C(Ω₂+σ₂,σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂,C(Ω₂+σ₂,σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,}2`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+C(Ω₂+σ₂,σ),C(Ω₂+σ₂,σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,3^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+σ₂,C(Ω₂+σ₂,σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+σ₂+1,σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂+C(Ω₂+σ₂+C(Ω₂+σ₂,σ),σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂2,0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,1`,,2^,,}1 {1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂2+C(Ω₂,C(Ω₂,σ)),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,1`,,2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂2+C(Ω₂+σ₂,σ),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,1`,,2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₂2+C(Ω₂+σ₂2,σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2`,,1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂2+C(Ω₂,C(Ω₂+σ₂2,σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂2+C(Ω₂+σ₂,C(Ω₂+σ₂2,σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,1`,,3^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂2+C(Ω₂+σ₂2,C(Ω₂+σ₂2,σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,1`,,1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂2+C(Ω₂+σ₂2+1,σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,1`,,1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₂3,0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ₂+1),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1`,,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(σ₂2),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1` `,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂,σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1` `,,1` `,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂,σ₂),σ₂)2,0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{2` `,,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(C(C(Ω₂,σ₂),σ₂)+1),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1` `,,3^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂,σ₂),C(C(Ω₂,σ₂),σ₂)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1` `,,1` `,,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂,σ₂)2,σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1` ` `,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂,C(Ω₂,σ₂)),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+1,σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1,,1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(Ω₂,σ)+1,σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1,,`1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(Ω₂,C(Ω₂,σ)),σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1,,`1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(Ω₂+σ₂,σ),σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1,,`1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1` `,,2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(Ω₂+C(C(Ω₂,σ₂),σ₂),σ),σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1`,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ₂,σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1` `,,2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂,σ₂),σ₂),σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1{1,,`1`,,2^,,}2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+σ₂,σ₂),σ₂),σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ₃,σ₂),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(σ₃,σ₂)+C(Ω₂+C(σ₃,σ₂),σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ₃,σ₂)+C(Ω₂+C(σ₃,σ₂)+1,σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ₃,σ₂)+σ₂,0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,2^,,}1{1,,`1` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ₃,σ₂)2,0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1` `,,2{1,,`1` `,,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂,σ₂),C(σ₃,σ₂)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1{1,,`1`,,2^,,}2{1,,`1` `,,2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ₂,σ₂),C(σ₃,σ₂)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1{1,,`1` `,,2^,,}3^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ₃,C(σ₃,σ₂)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1{1,,`1` `,,2^,,}1,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ₃+1,σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`2` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂,σ₃),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,3^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ₄,σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+1,0),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0),0),0)

Here’re some approximations, to make the comparisons above more simple:

The double comma approximately corresponds to C(Ω₂,C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^,,} approximately corresponds to C(Ω₂,C(Ω₂,C(Ω₂2,0)))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}3^,,} approximately corresponds to C(Ω₂,C(Ω₂,C(Ω₂,C(Ω₂2,0))))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,2^,,} approximately corresponds to C(Ω₂+1,C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,,2^,,} approximately corresponds to C(Ω₂+C(Ω₂,C(Ω₂2,0)),C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,,2^,,}2^,,} approximately corresponds to C(Ω₂+C(Ω₂+C(Ω₂,C(Ω₂2,0)),C(Ω₂2,0)),C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,} approximately corresponds to C(Ω₂+C(Ω₂2,C(Ω₂2,0)),C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1` `,,2^,,} approximately corresponds to C(Ω₂+C(C(Ω₂,C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1`,,2^,,}2^,,} approximately corresponds to C(Ω₂+C(C(Ω₂+C(Ω₂2,C(Ω₂2,0)),C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,2^,,}2^,,} approximately corresponds to C(Ω₂+C(C(Ω₂2,C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,3^,,}2^,,} approximately corresponds to C(Ω₂+C(C(Ω₂2,C(Ω₂2,C(Ω₂2,C(Ω₂2,0)))),C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,2^,,}2^,,} approximately corresponds to C(Ω₂+C(C(Ω₂2+1,0),C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,0))

Up to a C(Ω₂2,C(Ω₂2,C(Ω₂2,0)))

Now let separator ♦ = {1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}2} and let ordinal σ = σ₁ = C(Ω₂2,0), and σ_n+1 = C(Ω₂2,σ_n).

{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0),0),0)
{1{1,,1,,1,2}2{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0)+C(Ω₂+C(Ω₂,σ)+1,0),0),0)
{1{1{1,,`1{1,,`1,,`2^,,}2^,,}2}2{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0)+C(Ω₂+σ₂,0),0),0)
{1{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,2^,,}2^,,}2}2 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0)+C(Ω₂+C(C(Ω₂2+1,0),σ₂),0),0),0)
{1{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1♦2^,,}2^,,}2}2 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0),0),σ₂),0),0),0)
{1,,1,,1,2{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1♦2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+C(Ω₂,σ)+1,C(Ω₂+C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0),0),σ₂),0)),0),σ),C(Ω₂+C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0),0),σ₂),0)),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1♦2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0),0),σ₂)+1,0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1♦1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0)+C(Ω₂+C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0)+1,0),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1♦1♦2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),0)2,0),0)
{1,,1,,1,2{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ)+1,C(Ω₂+C(Ω₂,σ₂),0)),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,2^,,}2^,,}2 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+1,0),σ₂),C(Ω₂+C(Ω₂,σ₂),0)),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}3} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂),C(Ω₂+C(Ω₂,σ₂),0)),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+1,0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(σ₂,C(Ω₂,σ)),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}1 {1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(Ω₂,C(Ω₂,σ)),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(Ω₂+1,σ),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(Ω₂+σ₂,σ),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(Ω₂+C(C(Ω₂+1,σ₂),σ₂),σ),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1`,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(Ω₂+C(C(Ω₂+σ₂,σ₂),σ₂),σ),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(Ω₂+C(σ₃,σ₂),σ),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(Ω₂+C(C(Ω₂2+1,0),σ₂),σ),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(Ω₂+C(Ω₂,σ₂),σ),0),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(σ₂,C(Ω₂+C(Ω₂,σ₂),σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2{1,,`1` `,,1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(Ω₂,C(Ω₂+C(Ω₂,σ₂),σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2{1,,`1` `,,1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(Ω₂+σ₂,C(Ω₂+C(Ω₂,σ₂),σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,2^,,}2{1,,`1` `,,1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(Ω₂+C(σ₃,σ₂),C(Ω₂+C(Ω₂,σ₂),σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}3^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(Ω₂+C(Ω₂,σ₂),C(Ω₂+C(Ω₂,σ₂),σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(Ω₂+C(Ω₂,σ₂)+1,σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+σ₂,0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}1{1,,`1`,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(C(Ω₂+σ₂,σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}1{1,,`1` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(C(Ω₂+C(Ω₂,σ₂),σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}1{1,,`1` `,,1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(C(Ω₂+C(Ω₂,σ₂)+σ,σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1`,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(C(Ω₂+C(Ω₂,σ₂)+σ₂,σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1{1{1,,`1` `,,2^,,}2^`,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(C(Ω₂+C(Ω₂,σ₂)+C(C(Ω₂+C(Ω₂,σ₂),σ₂),σ₂),σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(σ₃,σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1` `,,1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)+C(C(Ω₂2+1,0),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1` `,,1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)2,0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1` `,,1` `,,1,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₂)3,0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{2^{` `,,}}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(C(Ω₂,σ₂)+1),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1{1,,`1,2^,,}2^{` `,,}}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+1,σ₂),C(Ω₂,σ₂)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1{1,,`1`,,2^,,}2^{` `,,}}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ₂,σ₂),C(Ω₂,σ₂)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1{1,,`1` `,,2^,,}2^{` `,,}}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(σ₃,σ₂),σ₂),C(Ω₂,σ₂)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1{1,,`1` `,,1,,2^,,}2^{` `,,}}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(Ω₂,σ₂),σ₂),C(Ω₂,σ₂)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1{1,,`1{1{1,,`1` `,,1,,2^,,}2^{` `,,}}2^,,}2^{` `,,}}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+C(Ω₂,σ₂),σ₂),C(Ω₂,σ₂)),σ₂),C(Ω₂,σ₂)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` ` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ₃,C(Ω₂,σ₂)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` ` ` `,,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ₃,C(Ω₂,C(Ω₂,σ₂))),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1{1,,`1{1,,`1,,`2^,,}2^,,}2^,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂+σ₂,σ),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1,,`1{1,,`1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,2^,,}2^,,}2^,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂+C(Ω₂+1,σ₂),σ),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1`,,2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ₂,σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1{1,,`1,2^,,}2^`,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂+1,σ₂),σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1{1,,`1`,,2^,,}2^`,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂+σ₂,σ₂),σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1{1,,`1{1,,`1,2^,,}2^,,}2^`,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂+C(Ω₂+1,σ₂),σ₂),σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1{1,,`1{1,,`1`,,2^,,}2^,,}2^`,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂+C(Ω₂+σ₂,σ₂),σ₂),σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1` `,,2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(σ₃,σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1` ` `,,2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(σ₃,C(Ω₂,σ₂)),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1,,`1,2^,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂+1,σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1,,`1{1,,`1,2^,,}2^,,}2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂+C(Ω₂+1,σ₂),σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃,0),0),0)

Here’re some approximations, to make the comparisons above more simple:

{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1,,2^,,}2^,,} approximately corresponds to C(Ω₂+C(Ω₂,C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,1` `,,1,,2^,,}2^,,} approximately corresponds to C(Ω₂+C(Ω₂,C(Ω₂2,C(Ω₂2,0)))2,C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` ` `,,2^,,}2^,,} approximately corresponds to C(Ω₂+C(C(Ω₂2,C(Ω₂2,C(Ω₂2,0))),C(Ω₂,C(Ω₂2,C(Ω₂2,0)))),C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` ` ` `,,2^,,}2^,,} approximately corresponds to C(Ω₂+C(C(Ω₂2,C(Ω₂2,C(Ω₂2,0))),C(Ω₂,C(Ω₂,C(Ω₂2,C(Ω₂2,0))))),C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,2^,,}2^,,}2^,,} approximately corresponds to C(Ω₂+C(Ω₂+1,C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1`,,2^,,}2^,,}2^,,} approximately corresponds to C(Ω₂+C(Ω₂+C(Ω₂2,C(Ω₂2,0)),C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1,,`1,2^,,}2^,,}2^,,}2^,,} approximately corresponds to C(Ω₂+C(Ω₂+C(Ω₂+1,C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,0))

The C(Ω₂2,C(Ω₂2,0)) seems to correspond to the `,, (i.e. {1,,`2^,,}) in {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{ ____ ^`,,}2^,,}. And C(Ω₂,C(Ω₂2,C(Ω₂2,0))) seems to correspond to {1,,`3^,,}, C(Ω₂,C(Ω₂,C(Ω₂2,C(Ω₂2,0)))) seems to correspond to {1,,`4^,,}, C(Ω₂+1,C(Ω₂2,C(Ω₂2,0))) seems to correspond to {1,,`1,2^,,}, and C(Ω₂+C(Ω₂2,C(Ω₂2,0)),C(Ω₂2,C(Ω₂2,0))) seems to correspond to {1,,`1`,,2^,,}. But those will be weaken in next comparisons.

Up to a C(Ω₂2+C(Ω₂2,0),0)

Now let ordinal σ = σ₁ = C(Ω₂2,0), and σ_n+1 = C(Ω₂2,σ_n).

{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+1,0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(Ω₂+σ₂,σ),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(Ω₂+σ₃,σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2{1,,`1{1,,`1,,`2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(Ω₂,C(Ω₂+σ₃,σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}3^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(Ω₂+σ₃,C(Ω₂+σ₃,σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}1,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(Ω₂+σ₃+1,σ),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+σ₂,0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}1{1,,`1,2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(C(Ω₂+1,σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(C(Ω₂+C(Ω₂+1,σ₂),σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(σ₃,σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1,,`1{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(σ₃,σ₂)2,0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{2{1,,`1{1,,`1,,`2^,,}2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+ω^(C(σ₃,σ₂)+1),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1` `,,2{1,,`1{1,,`1,,`2^,,}2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(C(Ω₂,σ₂),C(σ₃,σ₂)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1{1,,`1{1,,`1,,`2^,,}2^,,}3^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(σ₃,C(σ₃,σ₂)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1{1,,`1{1,,`1,,`2^,,}2^,,}1,2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(σ₃+1,σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1{1,,`1{1,,`1,,`2^,,}2^,,}2,,`1{1,,`1,,`2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(σ₃2,σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`2{1,,`1,,`2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(C(Ω₂,σ₃),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,2^,,}2{1,,`1,,`2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(C(Ω₂+C(Ω₂+1,σ₂),σ₃),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}2{1,,`1,,`2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(σ₄,σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,2{1,,`1,,`2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(C(Ω₂2+1,0),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(Ω₂,σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(Ω₂,σ₂)+σ₂,0),0),0)
{1{2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^`,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+ω^(C(Ω₂,σ₂)+1),0),0),0)
{1`,,2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+ω^(C(Ω₂,σ₂)+σ₂),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^`,,}2 {1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+ω^(C(Ω₂,σ₂)2),0),0),0)
{1` `,,2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(C(Ω₂,C(Ω₂,σ₂)),C(Ω₂,σ₂)),0),0),0)
{1{1,,`1`,,2^,,}2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(C(Ω₂+σ₂,σ₂),C(Ω₂,σ₂)),0),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(σ₃,C(Ω₂,σ₂)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}3^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(Ω₂,C(Ω₂,σ₂)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(Ω₂+1,σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(Ω₂+σ₂,σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^`,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(Ω₂+C(Ω₂,σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^`,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(Ω₂+C(Ω₂+σ₂,σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1` `,,2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(Ω₂+σ₃,σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1` `,,1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1` `,,2^`,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃+C(Ω₂+σ₃+C(Ω₂+σ₃,σ₂),σ₂),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1` `,,1` `,,2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₃2,0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1,2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+1,σ₃),σ₃),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1`,,2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ₂,σ₃),σ₃),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` `,,2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+σ₃,σ₃),σ₃),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1{1,,`1` `,,2^,,}2^{` `,,}}2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+σ₃,σ₃),σ₃),σ₃),σ₃),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` ` `,,2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+C(σ₄,σ₃),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` ` `,,1,2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+1,0),σ₃),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1` ` `,,1,,2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ₃),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,2^,,}2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ₃),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1` `,,2^,,}2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+σ₃,σ₃),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1,,`1` `,,2^,,}2^,,}2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂+σ₃,σ₃),σ₃),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₄,0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₄+C(Ω₂,σ₃),0),0),0)
{1{2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^`,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₄+ω^(C(Ω₂,σ₃)+1),0),0),0)
{1` `,,2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+σ₄+ω^(C(Ω₂,σ₃)+σ₃),0),0),0)

Generally, the recursion level of {1{1,,`k^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} is between C(C(Ω₂2+C(Ω₂+σ_k+1,0),0),0) and C(C(Ω₂2+C(Ω₂+σ_k+2,0),0),0) (where σ₁ = C(Ω₂2,0), and σ_n+1 = C(Ω₂2,σ_n)), so {1{1,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+1,0),0),0),0).

{1{1{1,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+1,0)+1,0),0),0)
{1{1{1,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,,1,2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+1,0)+C(Ω₂,C(Ω₂2,0))+1,0),0),0)
{1{1{1,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1{1,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+1,0)+C(Ω₂+C(Ω₂2+1,0),C(Ω₂2,0)),0),0),0)
{1,,2{1,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+1,0)+ω^(C(Ω₂+C(Ω₂2+1,0),C(Ω₂2,0))+C(Ω₂,C(Ω₂2,0))),0),0),0)
{1`,,2{1,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+1,0)+ω^(C(Ω₂+C(Ω₂2+1,0),C(Ω₂2,C(Ω₂2,0)))+C(Ω₂2,C(Ω₂2,0))),0),0),0)
{1` `,,2{1,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+1,0)+ω^(C(Ω₂+C(Ω₂2+1,0),C(Ω₂2,C(Ω₂2,C(Ω₂2,0))))+C(Ω₂2,C(Ω₂2,C(Ω₂2,0)))),0),0),0)
{1{1,,`1,2^,,}3,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+1,0)2,0),0),0)
{1{1{1,,`2,2^,,}2,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂,C(Ω₂2+1,0)),C(Ω₂2+1,0)),0),0),0)
{1{1{1,,`1{1,,`1,2^,,}2^,,}2,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(Ω₂2+1,0),C(Ω₂2+1,0)),C(Ω₂2+1,0)),0),0),0)
{1{1{1,,`1{1{1,,`1{1,,`1,2^,,}2^,,}2,,`1,2^,,}2^,,}2,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂+C(Ω₂2+1,0),C(Ω₂2+1,0)),C(Ω₂2+1,0)),C(Ω₂2+1,0)),C(Ω₂2+1,0)),0),0),0)
{1{1{1,,`1{1,,`2,2^,,}2^,,}2,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,C(Ω₂2+1,0)),C(Ω₂2+1,0)),0),0),0)
{1{1{1,,`1{1,,`2,2^,,}1,2^,,}2,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+1,C(Ω₂2+1,0)),C(Ω₂2+1,0)),0),0),0)
{1{1{1,,`1{1,,`2,2^,,}1,1,2^,,}2,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+2,0),C(Ω₂2+1,0)),0),0),0)
{1{1{1,,`1{1,,`2,2^,,}1,,2^,,}2,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,C(Ω₂2+1,0)),0),0),0)
{1{1{1,,`1{1,,`3,2^,,}2^,,}2,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,C(Ω₂2+1,0)),C(Ω₂,C(Ω₂2+1,0))),0),0),0)
{1{1{1,,`1{1,,`1,3^,,}2^,,}2,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,C(Ω₂2+1,0)),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,2^,,}2^,,}2^,,}2,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂2+1,0),C(Ω₂2+1,0)),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1{1,,`1,2^,,}2^,,}2^,,}2^,,}2,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂+C(Ω₂2+1,0),C(Ω₂2+1,0)),C(Ω₂2+1,0)),0),0),0)
{1{1{1,,`1{1,,`1,,`2^,,}2^,,}2,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2+1,0)),0),0),0)
{1{1,,`1,2^,,}2{1{1,,`1{1,,`1,,`2^,,}2^,,}2,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2+1,0))+C(Ω₂2+1,0),0),0),0)
{1{1{1,,`1{1,,`1,,`2^,,}2^,,}2,,`1,2^,,}3,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2+1,0))+C(C(Ω₂2,C(Ω₂2+1,0)),C(Ω₂2+1,0)),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}2{1,,`1,,`2^,,}2^,,}2,,`1,2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2+1,0))+C(C(Ω₂2,C(Ω₂2,C(Ω₂2+1,0))),C(Ω₂2+1,0)),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2,,`1,2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2+1,0))+C(Ω₂,C(Ω₂2+1,0)),0),0),0)
{1{1,,`1,2^,,}2{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2,,`1,2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2+1,0))+C(Ω₂,C(Ω₂2+1,0))+C(Ω₂2+1,0),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2,,`1,2^,,} 3,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2+1,0))+C(Ω₂,C(Ω₂2+1,0))2,0),0),0)
{1{2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2,,`1,2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2+1,0))+ω^ω^(C(Ω₂,C(Ω₂2+1,0))+1),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}3,,`1,2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2+1,0))+C(Ω₂,C(Ω₂,C(Ω₂2+1,0))),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1,2^,,}2,,`1,2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2+1,0))+C(Ω₂+C(Ω₂2+1,0),C(Ω₂2+1,0)),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2,,`1,2^,,}2,,`1,2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2+1,0))+C(Ω₂+C(Ω₂,C(Ω₂2+1,0)),C(Ω₂2+1,0)),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`2,2^,,}2,,`1,2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2+1,0))2,0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`3,2^,,}2^,,}2,,`1,2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,C(Ω₂2,C(Ω₂2+1,0))),C(Ω₂2,C(Ω₂2+1,0))),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`4,2^,,}2^,,}2,,`1,2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,C(Ω₂2,C(Ω₂2+1,0))),C(Ω₂,C(Ω₂2,C(Ω₂2+1,0)))),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,3^,,}2^,,}2,,`1,2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,C(Ω₂2,C(Ω₂2+1,0))),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1{1,,`1{1,,`1,,`2^,,}2^,,}2,,`1,2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2,C(Ω₂2+1,0))),0),0),0)
{1{1{2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2,,`1,2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(C(Ω₂2,C(Ω₂2,C(Ω₂2+1,0)))+1),0),0),0)
{1{1,,`2,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(C(Ω₂2,C(Ω₂2,C(Ω₂2+1,0)))+C(Ω₂2,C(Ω₂2+1,0))),0),0),0)
{1{1,,`3,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+ω^(C(Ω₂2,C(Ω₂2,C(Ω₂2,C(Ω₂2+1,0))))+C(Ω₂2,C(Ω₂2,C(Ω₂2+1,0)))),0),0),0)
{1{1,,`1,3^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+1,C(Ω₂2+1,0)),0),0),0)
{1{1,,`1,1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+2,0),0),0),0)
{1{1,,`1{1{1{1,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+C(Ω₂+C(Ω₂2+1,0),0),0),0),0),0)
{1{1,,`1,,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂2,0),0),0)

Up to here, some approximations make the comparisons above more simple:

The double comma approximately corresponds to C(Ω₂,C(Ω₂2,0))
`,, approximately corresponds to C(Ω₂2,C(Ω₂2,0))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^`,,} approximately corresponds to C(Ω₂,C(Ω₂2,C(Ω₂2,0)))
` `,, approximately corresponds to C(Ω₂2,C(Ω₂2,C(Ω₂2,0)))
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2^{` `,,}} approximately corresponds to C(Ω₂,C(Ω₂2,C(Ω₂2,C(Ω₂2,0))))
{1,,`1,2^,,} approximately corresponds to C(Ω₂2+1,0)
{1,,`2,2^,,} approximately corresponds to C(Ω₂2,C(Ω₂2+1,0))
{1,,`3,2^,,} approximately corresponds to C(Ω₂2,C(Ω₂2,C(Ω₂2+1,0)))

Beyond C(Ω₂2+C(Ω₂2,0),0)

Now let separator ♦ = {1{1{1,,`1,,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} and ♥ = {1{1,,`1♦2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} and let ordinal σ = C(Ω₂2,0).

{1,,1{1{1♥2}2,,1{1,,1,,2}2}2{1,,1,,2}2} has recursion level C(C(Ω₂2+σ,0),0)
{1,,1{1{1♥2}2,,1{1,,1,,2}2}1,2{1,,1,,2}2} has recursion level C(C(Ω₂2+σ+1,0),0)
{1,,1{2{1,,1{1♥2}2}2,,1{1,,1,,2}2}2{1,,1,,2}2} has recursion level C(C(Ω₂2+σ+ω^(C(C(Ω₂2+σ,0),C(Ω₂+σ,0))+1),0),0)
{1,,2{1♥2}2} has recursion level C(C(Ω₂2+σ+C(C(Ω₂,C(Ω₂2+σ,0)),C(Ω₂+σ,0)),0),0)
{1,,1{1,,1{1♥2}2}2{1♥2}2} has recursion level C(C(Ω₂2+σ+C(C(Ω₂2+σ,C(Ω₂2+σ,0)),C(Ω₂+σ,0)),0),0)
{1,,1{1,,1{1♥2}2}1,2{1♥2}2} has recursion level C(C(Ω₂2+σ+C(C(Ω₂2+σ+1,0),C(Ω₂+σ,0)),0),0)
{1,,1{1,,1{1♥2}2}1{1,,2{1,,1,,2}2}2{1♥2}2} has recursion level C(C(Ω₂2+σ+C(Ω₂,C(Ω₂+σ,0)),0),0)
{1,,1{1,,1{1♥2}2}1{1,,1{1,,1,,2}1,2}2{1♥2}2} has recursion level C(C(Ω₂2+σ+C(Ω₂+σ+1,0),0),0)
{1,,1{1,,1{1♥2}2}1{1,,1{1,,1{1,,2,,2}1,2,,2}2}2{1♥2}2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+1,0),σ),0),0),0)
{1,,1{1,,1{1♥2}2}1{1,,1{1♥2}2}2{1♥2}2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+σ,0),σ),0),0),0)
{1,,1{1,,1,,2}2{1♥2}2} has recursion level C(C(Ω₂2+σ+C(σ,C(Ω₂+C(C(Ω₂2+σ,0),σ),0)),0),0)
{1,,1{1♥2}3} has recursion level C(C(Ω₂2+σ+C(C(Ω₂2+σ,0),C(Ω₂+C(C(Ω₂2+σ,0),σ),0)),0),0)
{1,,1{1♥2}1,2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+σ,0),σ)+1,0),0),0)
{1{1,,1,,2}2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+ω^(C(C(Ω₂2+σ,0),σ)+σ),0),0),0)
{1{1,,1{1,,2,,2}1{1,,1,,2}2,,2}2,,1{1,,2,,2}1{1{1♥2}2,,1,,2}2,,2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+σ,0)+C(Ω₂2+C(Ω₂+C(Ω₂,σ),0),0),σ),0),0),0)
{1{1,,1{1,,2,,2}1{1{1,,1{1,,1,,3}2,,2}2,,1,,2}2,,2}2,,1{1,,2,,2}1{1{1♥2}2,,1,,2}2,,2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+σ,0)+C(Ω₂2+C(σ,C(Ω₂+C(Ω₂,σ),0)),0),σ),0),0),0)
{1{1,,1{1,,2,,2}1{1{1,,1,,1,2}2,,1,,2}2,,2}2,,1{1,,2,,2}1{1{1♥2}2,,1,,2}2,,2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+σ,0)+C(Ω₂2+C(Ω₂+C(Ω₂,σ)+1,0),0),σ),0),0),0)
{1{1,,1{1,,2,,2}1{1{1{1,,`1{1,,`1,,`2^,,}2^,,}2}2,,1,,2}2,,2}2,,1{1,,2,,2}1{1{1♥2}2,,1,,2}2,,2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+σ,0)+C(Ω₂2+C(Ω₂+C(Ω₂2,σ),0),0),σ),0),0),0)
{1{1,,1{1,,2,,2}1{1{1♥2}2,,1,,2}2,,2}2,,1{1,,2,,2}1{1{1♥2}2,,1,,2}2,,2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+σ,0)2,σ),0),0),0)
{1,,2{1,,2,,2}1{1{1♥2}2,,1,,2}2,,2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂,C(Ω₂2+σ,0)),σ),0),0),0)
{1,,1{1,,2,,2}1{1{1♥2}2,,1,,2}1,2,,2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+σ+1,0),σ),0),0),0)
{1,,1{1,,2,,2}1{1{1♥2}2,,1,,2}1{1,,1,,2}2,,2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂,σ),0),0),0)
{1{1,,1,,1,2}2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂,σ)+1,0),0),0)
{1{1{1,,`1`,,2^,,}2}2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2,σ),C(Ω₂,σ)),0),0),0)
{1{1{1,,`1`,,1{1♥2}2^,,}2}2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+σ,0),C(Ω₂,σ)),0),0),0)
{1{1{1,,`1`,,1,,2^,,}2}2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂,C(Ω₂,σ)),0),0),0)
{1{1{1,,`1` `,,2^,,}2}2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2,σ),C(Ω₂,C(Ω₂,σ))),0),0),0)
{1{1{1,,`1{1,,`1,2^,,}2^,,}2}2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂+1,σ),0),0),0)
{1{1{1,,`1{1,,`1,,`2^,,}2^,,}2}2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2,σ),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2}2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2,σ)+C(Ω₂,C(Ω₂,σ)),0),0),0)
{1{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,1`,,2^,,}2}2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2,σ)2,0),0),0)
{1{1{1{1,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2}2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+1,0),0),0),0)
{1{1♥2}2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0),0),0),0)
{1,,1,,2♥2} has recursion level C(C(Ω₂2+σ+C(σ,C(Ω₂+C(Ω₂2+σ,0),0)),0),0)
{1,,1{1,,2,,2♥2}1,2,,2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+1,0),σ),C(Ω₂+C(Ω₂2+σ,0),0)),0),0)
{1,,1{1,,2,,2♥2}1{1,,1,,2♥2}2,,2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+C(Ω₂+C(Ω₂,σ),C(Ω₂+C(Ω₂2+σ,0),0)),0),σ),C(Ω₂+C(Ω₂2+σ,0),0)),0),0)
{1,,1,,1,2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+C(Ω₂+C(Ω₂,σ)+1,C(Ω₂+C(Ω₂2+σ,0),0)),0),σ),C(Ω₂+C(Ω₂2+σ,0),0)),0),0)
{1{1{1,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+C(Ω₂+C(Ω₂2+1,0),C(Ω₂+C(Ω₂2+σ,0),0)),0),σ),C(Ω₂+C(Ω₂2+σ,0),0)),0),0)
{1♥3} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(C(Ω₂2+σ,0),σ),C(Ω₂+C(Ω₂2+σ,0),0)),0),0)
{1{1♥3}2♥3} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0),C(Ω₂+C(Ω₂2+σ,0),0)),0),0)
{1♥1,2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+1,0),0),0)
{1♥1,,1,2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(Ω₂,σ)+1,0),0),0)
{1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(C(Ω₂2+1,0),C(Ω₂,σ)),0),0),0)
{1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1{1♥2}2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(C(Ω₂2+C(Ω₂+C(Ω₂2+σ,0),0),0),C(Ω₂,σ)),0),0),0)
{1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(C(Ω₂2+σ,0),C(Ω₂,σ)),0),0),0) (this time, the σ in C(Ω₂+C(Ω₂2+σ,0)+C(C(Ω₂2+σ,0),C(Ω₂,σ)),0) works as a 1-separator)
{1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1 {1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} 2{1,,`1,,`2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(C(Ω₂2+σ,0),C(Ω₂,σ))+1,0),0),0)
{1♥1{2{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1 {1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} 2{1,,`1,,`2^,,}2^,,}2^,,}2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+ω^(C(C(Ω₂2+σ,0),C(Ω₂,σ))+1),0),0),0)
{1♥1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1 {1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} 2{1,,`1,,`2^,,}2^,,}1,2^,,}2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(C(Ω₂2+σ,0)+1,C(Ω₂,σ)),0),0),0)
{1♥1{1,,`2{1,,`1{1,,`1,,`2^,,}2^,,}1 {1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} 2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(C(Ω₂,C(Ω₂2+σ,0)),C(Ω₂,σ)),0),0),0)
{1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}2 {1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} 2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(C(Ω₂2,C(Ω₂2+σ,0)),C(Ω₂,σ)),0),0),0)
{1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1 {1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} 1,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(C(Ω₂2+σ+1,0),C(Ω₂,σ)),0),0),0)
{1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1 {1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2}1 {1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} 2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(Ω₂,C(Ω₂,σ)),0),0),0)
{1♥1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(Ω₂,C(Ω₂,σ))+1,0),0),0) (however, the extra 1-separator doesn’t affect the strength much)
{1♥1{1{1,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(Ω₂+C(Ω₂2+1,0),σ),0),0),0)
{1♥1♥2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(Ω₂+C(Ω₂2+σ,0),σ),0),0),0)
{1{2♥2^,,}2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+ω^(C(Ω₂+C(Ω₂2+σ,0),σ)+1),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,2{1,,`1,,`2^,,}2^,,}2♥2^,,} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(C(Ω₂2+1,0),C(Ω₂+C(Ω₂2+σ,0),σ)),0),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2♥2^,,} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(C(Ω₂2+σ,0),C(Ω₂+C(Ω₂2+σ,0),σ)),0),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2♥2^,,}1,2} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(Ω₂,C(Ω₂+C(Ω₂2+σ,0),σ))+1,0),0),0)
{1♥1,2^,,} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(Ω₂+C(Ω₂2+σ,0)+1,σ),0),0),0)
{1♥1`,,2^,,} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(Ω₂2,σ),0),0),0)
{1{1,,`1,2^,,}2{1,,`1♦2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)+C(Ω₂2+1,0),0),0),0)
{1{1,,`1♦2^,,}3,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,0)2,0),0),0)
{1{1,,`1,2♦2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+1,C(Ω₂2+σ,0)),0),0),0)
{1{1,,`1♦3^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ,C(Ω₂2+σ,0)),0),0),0)
{1{1,,`1♦1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+σ+C(Ω₂+C(Ω₂2+σ+1,0),0),0),0)
{1{1,,`1♦1♦2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+σ2,0),0)
{1,,2{1{1,,`1,,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(C(Ω₂,σ),σ),0),0)
{1,,1,2{1{1,,`1,,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(C(Ω₂+1,σ),σ),0),0)
{1,,1,,2{1{1,,`1,,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(C(Ω₂2,σ),σ),0),0)

At this stage, C(Ω₂+____,0) ordinals correspond to {1{1{1,,`1 A 2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} with lv(A) < lv(,,); and C(Ω₂2,0) is the supremum of them, so it corresponds to {1{1{1,,`1,,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2}. When it reduces, the double comma (red) is the 2-separator, {1{1{1,,`1,,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} is where it drops down to (1-separator).

Now let separator ◊ = {1{1,,`1,,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} and let ordinal σ = C(Ω₂2,0).

{1{1,,1{1,,1,,2◊2}2◊2}2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂2,σ),σ),0),0)
{1{1,,2◊2}2{1,,1{1,,1,,2◊2}2◊2}2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂,σ),C(C(Ω₂2,σ),σ)),0),0)
{1{1,,1{1,,1,,2◊2}2◊2}3◊2} has recursion level C(C(Ω₂2+C(C(Ω₂2,σ),C(C(Ω₂2,σ),σ)),0),0)
{1{1,,1{1,,1,,2◊2}2◊2}1,2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂2,σ)+1,σ),0),0)
{1{1,,1{1,,1,,2◊2}2◊2}2,,1{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂2,σ)2,σ),0),0)
{1,,2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂,C(Ω₂2,σ)),σ),0),0)
{1,,1{1,,1,2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂+C(Ω₂+1,σ),C(Ω₂2,σ)),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂2,C(Ω₂2,σ)),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1,2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂2+1,0),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1{1{1,,`1{1◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2}2 {1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂2+C(Ω₂+C(Ω₂2+σ,0),0),0),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂2+σ,0),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1◊2}2{1,,1,,2◊2}2◊2}2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂2+C(C(Ω₂2+σ,0),σ),0),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂,σ),0),0)

Now let separator ◊ = {1{1,,`1,,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} and ♦ = {1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2} and ♥ = {1{1,,`1♦2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} and let ordinal σ = C(Ω₂2,0).

{1,,1{1{1♥2}2,,1{1,,1,,2}2}1,2{1,,1,,2}2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+1,0),0)
{1,,1{1{1♥2}2,,1{1,,1,,2}2}1{1{1♥2}2,,1{1,,1,,2}2}2{1,,1,,2}2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(C(Ω₂2+C(Ω₂,σ),0),C(Ω₂+σ,0)),0),0)
{1,,1{2{1,,1{1♥2}2}2,,1{1,,1,,2}2}2{1,,1,,2}2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+ω^(C(C(Ω₂2+C(Ω₂,σ),0),C(Ω₂+σ,0))+1),0),0)
{1,,2{1♥2}2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(C(Ω₂,C(Ω₂2+C(Ω₂,σ),0)),C(Ω₂+σ,0)),0),0)
{1,,1{1,,1{1♥2}2}1,2{1♥2}2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(C(Ω₂2+C(Ω₂,σ)+1,0),C(Ω₂+σ,0)),0),0)
{1,,1{1,,1{1♥2}2}1{1,,2{1,,1,,2}2}2{1♥2}2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂,C(Ω₂+σ,0)),0),0)
{1,,1{1,,1{1♥2}2}1{1,,1{1{1{1,,`1{1◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2}2}2{1♥2}2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(C(Ω₂2+σ,0),σ),0),0),0)
{1,,1{1,,1{1♥2}2}1{1,,1{1♥2}2}2{1♥2}2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(C(Ω₂2+C(Ω₂,σ),0),σ),0),0),0)
{1,,1{1♥2}1,2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(C(Ω₂2+C(Ω₂,σ),0),σ)+1,0),0),0)
{1{1,,1,,2}2♥2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+ω^(C(C(Ω₂2+C(Ω₂,σ),0),σ)+1),0),0),0)
{1{1,,1,,1,2}2♥2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(Ω₂,σ)+1,0),0),0)
{1{1{1,,`1`,,1{1♥2}2^,,}2}2♥2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(C(Ω₂2+C(Ω₂,σ),0),C(Ω₂,σ)),0),0),0)
{1{1{1,,`1`,,1,,2^,,}2}2♥2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(Ω₂,C(Ω₂,σ)),0),0),0)
{1{1{1{1,,`1{1◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2}2♥2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(Ω₂2+σ,0),0),0),0)
{1{1{1{1,,`1{1◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,2}2♥2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(Ω₂2+σ,0)+1,0),0),0)
{1 {1{1{1,,`1{1◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1 {1{1{1,,`1{1◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} 2{1,,`1,,`2^,,}2^,,}2} 2♥2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(Ω₂2+σ,0)+C(C(Ω₂2+σ,0),C(Ω₂,σ)),0),0),0)
{1 {1{1{1,,`1{1◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1 {1{1{1,,`1{1◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} 1,2{1,,`1,,`2^,,}2^,,}2} 2♥2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(Ω₂2+σ,0)+C(C(Ω₂2+σ+1,0),C(Ω₂,σ)),0),0),0)
{1 {1{1{1,,`1{1◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1 {2{1{1,,`1{1◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1 {1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} 2{1,,`1,,`2^,,}2^,,}2} 2♥2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(Ω₂2+σ,0)+C(C(Ω₂2+ω^(σ+1),0),C(Ω₂,σ)),0),0),0)

{1 {1{1{1,,`1{1◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2}2 {1{1,,`1{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(Ω₂2+σ,0),0),0),0)
{1 {1{1{1,,`1{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2} 2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2}2 {1{1,,`1{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(Ω₂2+C(Ω₂,σ),0),0),0),0)
{1,,1,,2{1{1,,`1{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(σ,C(Ω₂+C(Ω₂2+C(Ω₂,σ),0),0)),0),0)
{1{1{1,,`1{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(Ω₂2+C(Ω₂,σ),0)+1,0),0),0)
{1{1,,`1{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}1,2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(Ω₂+C(Ω₂2+C(Ω₂,σ)+1,0),0),0),0)
{1{1,,`1{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}1{1◊2}2^,,} 2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂,σ)+σ,0),0)
{1{1,,`1 {1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}1 {1,,1{1,,1{1,,1,,2◊2}2◊2}1,2{1,,1,,2◊2}2◊2} 2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(C(Ω₂2+1,0),σ),0),0)
{1{1,,`1 {1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}1 {1,,1{1,,1{1,,1,,2◊2}2◊2}1{1◊2}2{1,,1,,2◊2}2◊2} 2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(C(Ω₂2+σ,0),σ),0),0)
{1{1,,`1 {1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}1 {1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2} 2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(C(Ω₂2+C(Ω₂,σ),0),σ),0),0)
{1{1,,2◊2}2{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(C(Ω₂,σ),C(C(Ω₂2+C(Ω₂,σ),0),σ)),0),0)
{1{1,,1{1,,1{1,,1,,2◊2}2◊2}1,2{1,,1,,2◊2}2◊2}2 {1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(C(Ω₂2+1,0),C(C(Ω₂2+C(Ω₂,σ),0),σ)),0),0)
{1{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1◊2}2{1,,1,,2◊2}2◊2}2 {1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(C(Ω₂2+σ,0),C(C(Ω₂2+C(Ω₂,σ),0),σ)),0),0)
{1{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}3◊2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(C(Ω₂2+C(Ω₂,σ),0),C(C(Ω₂2+C(Ω₂,σ),0),σ)),0),0)
{1{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}1,2◊2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(C(Ω₂2+C(Ω₂,σ),0)+1,σ),0),0)
{1,,2{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(C(Ω₂,C(Ω₂2+C(Ω₂,σ),0)),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}2{1,,2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(C(Ω₂2,C(Ω₂2+C(Ω₂,σ),0)),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}1,2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂,σ)+C(C(Ω₂2+C(Ω₂,σ)+1,0),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂,σ)2,0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1{1,,3◊2}2,,2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂,C(Ω₂,σ)),C(Ω₂,σ)),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,3◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂,C(Ω₂,σ)),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,1,2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+1,σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,1 {1{1{1,,`1{1◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} 2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂2+σ,0),0),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,1 {1{1{1,,`1 {1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2} 2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} 2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂2+C(Ω₂,σ),0),0),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,1{1◊2}2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+σ,σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,1 {1{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1◊2}2{1,,1,,2◊2}2◊2}2◊2} 2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+σ,0),σ),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,1 {1{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,2◊2}2{1,,1,,2◊2}2◊2}2◊2} 2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+C(Ω₂,σ),0),σ),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,1{1,,2◊2}2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,σ),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,1{1,,1,2◊2}2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,σ),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,1{1,,1{1,,1,2◊2}2◊2}2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂+1,σ),σ),σ),0),0)
{1,,1{1,,1{1,,1,,2◊2}2◊2}1{1,,1{1,,1,,2◊2}2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,σ),σ),0),0)
{1,,1{2,,1{1,,1,,2◊2}2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+ω^(C(Ω₂+C(Ω₂2,σ),σ)+1),0),0)
{1,,1{1{1,,2{1,,1,,2◊2}2◊2}2,,1{1,,1,,2◊2}2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂,C(Ω₂+C(Ω₂2,σ),σ)),C(Ω₂+C(Ω₂2,σ),σ)),0),0)
{1,,1{1{1,,1{1,,1{1,,1,,2◊2}2◊2}2{1,,1,,2◊2}2◊2}2,,1{1,,1,,2◊2}2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂+C(Ω₂+C(Ω₂2,σ),σ),C(Ω₂+C(Ω₂2,σ),σ)),C(Ω₂+C(Ω₂2,σ),σ)),0),0)
{1,,1{1,,2{1,,1,,2◊2}2◊2}2{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(C(Ω₂+C(Ω₂,C(Ω₂+C(Ω₂2,σ),σ)),C(Ω₂+C(Ω₂2,σ),σ)),C(Ω₂+C(Ω₂2,σ),σ)),0),0)
{1,,1{1,,1,,2◊2}3◊2} has recursion level C(C(Ω₂2+C(C(Ω₂2,σ),C(Ω₂+C(Ω₂2,σ),σ)),0),0)
{1,,1{1,,1{1,,1,,2◊2}3◊2}1{1,,1{1,,1,,2◊2}3◊2}2{1,,1,,2◊2}3◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,σ),C(Ω₂+C(Ω₂2,σ),σ)),0),0)
{1,,1{1,,1,,2◊2}4◊2} has recursion level C(C(Ω₂2+C(C(Ω₂2,σ),C(Ω₂+C(Ω₂2,σ),C(Ω₂+C(Ω₂2,σ),σ))),0),0)
{1,,1{1,,1,,2◊2}1,2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,σ)+1,σ),0),0)
{1,,1{1,,1,,2◊2}1{1◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,σ)+σ,σ),0),0)
{1,,1{1,,1,,2◊2}1{1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,σ)+C(Ω₂,σ),σ),0),0)
{1,,1{1,,1,,2◊2}1{1,,1{1,,1,,2◊2}2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,σ)+C(Ω₂+C(Ω₂2,σ),σ),σ),0),0)
{1,,1{1,,1,,2◊2}1{1,,1,,2◊2}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,σ)2,σ),0),0)
{1,,2,,2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂,C(Ω₂2,σ)),C(Ω₂2,σ)),σ),0),0)
{1,,1{1,,1,,2◊2}2,,2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(Ω₂2,σ),C(Ω₂2,σ)),C(Ω₂2,σ)),σ),0),0)
{1,,1{1{1,,2,,2◊2}2,,1,,2◊2}2,,2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(C(Ω₂,C(Ω₂2,σ)),C(Ω₂2,σ)),C(Ω₂2,σ)),C(Ω₂2,σ)),σ),0),0)
{1,,1{1,,2,,2◊2}2,,2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,C(Ω₂2,σ)),C(Ω₂2,σ)),σ),0),0)
{1,,1{1,,2,,2◊2}1,2,,2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+1,0),C(Ω₂2,σ)),σ),0),0)
{1,,1{1,,2,,2◊2}1{1◊2}2,,2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2+σ,0),C(Ω₂2,σ)),σ),0),0)
{1,,1{1,,2,,2◊2}1{1,,1,,2◊2}2,,2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,C(Ω₂2,σ)),σ),0),0)
{1,,1,,1,2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,C(Ω₂2,σ))+1,σ),0),0)
{1,,1,,1,,2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,C(Ω₂2,σ))+C(Ω₂2,σ),σ),0),0)
{1,,1,,1,,1,,2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂,C(Ω₂2,σ))2+C(Ω₂2,σ),σ),0),0)
{1{2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+ω^(C(Ω₂,C(Ω₂2,σ))+1),σ),0),0)
{1{1`,,2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂,C(Ω₂,C(Ω₂2,σ))),C(Ω₂,C(Ω₂2,σ))),σ),0),0)
{1{1,,`1,,2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂+C(Ω₂2,σ),C(Ω₂2,σ)),C(Ω₂,C(Ω₂2,σ))),σ),0),0)
{1{1,,`1`,,2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,C(Ω₂2,σ)),C(Ω₂,C(Ω₂2,σ))),σ),0),0)
{1{1,,`1` `,,2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(C(Ω₂2,C(Ω₂2,σ)),C(Ω₂,C(Ω₂,C(Ω₂2,σ)))),σ),0),0)
{1{1,,`1{1,,`1,2^,,}2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+1,C(Ω₂2,σ)),σ),0),0)
{1{1,,`1{1,,`1,,2^,,}2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂2,σ),C(Ω₂2,σ)),σ),0),0)
{1{1,,`1{1,,`1`,,2^,,}2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(C(Ω₂2,C(Ω₂2,σ)),C(Ω₂,C(Ω₂2,σ))),C(Ω₂2,σ)),σ),0),0)
{1{1,,`1{1,,`1{1,,`1,2^,,}2^,,}2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂+C(Ω₂+1,C(Ω₂2,σ)),C(Ω₂2,σ)),σ),0),0)
{1{1,,`1{1,,`1,,`2^,,}2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2,σ)),σ),0),0)
{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2,σ))+C(Ω₂,C(Ω₂,C(Ω₂2,σ))),σ),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2,σ))+C(Ω₂+1,C(Ω₂2,σ)),σ),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2,σ))+C(Ω₂+C(Ω₂2,C(Ω₂2,σ)),C(Ω₂2,σ)),σ),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1`,,1`,,2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2,σ))2,σ),0),0)
{1{1{1,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1` `,,1` `,,2^`,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2,C(Ω₂2,C(Ω₂2,σ)))2,σ),0),0)
{1{1{1,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+1,0),σ),0),0)
{1{1{1,,`1{1◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+σ,0),σ),0),0)
{1{1{1,,`1{1,,2◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+C(Ω₂,σ),0),σ),0),0)
{1{1{1,,`1 {1{1{1,,`1,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2◊2} 2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2◊2} has recursion level C(C(Ω₂2+C(Ω₂+C(Ω₂2+C(Ω₂+C(Ω₂2+1,0),σ),0),σ),0),0)
{1◊3} has recursion level C(C(Ω₂2+C(Ω₂2,σ),0),0)
{1◊4} has recursion level C(C(Ω₂2+C(Ω₂2,C(Ω₂2,σ)),0),0)
{1◊1,2} has recursion level C(C(Ω₂2+C(Ω₂2+1,0),0),0)
{1◊1{1◊2}2} has recursion level C(C(Ω₂2+C(Ω₂2+σ,0),0),0)
{1◊1{1◊1,2}2} has recursion level C(C(Ω₂2+C(Ω₂2+C(Ω₂2+1,0),0),0),0)
{1◊1,,2} has recursion level C(C(Ω₂3,0),0)

So {1{1{1,,`1,,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,,2} has recursion level C(C(Ω₂3,0),0).

Here’re some approximations, to make the comparisons above more simple:

{1◊2} (where ◊ = {1{1,,`1,,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}) approximately corresponds to C(Ω₂2,0)
{1{1{1,,`1{1◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} approximately corresponds to C(Ω₂+C(Ω₂2+C(Ω₂2,0),0),0)
{1,,2◊2} approximately corresponds to C(Ω₂,C(Ω₂2,0))
{1{1{1,,`1{1,,2◊2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} approximately corresponds to C(Ω₂+C(Ω₂2+C(Ω₂,C(Ω₂2,0)),0),0)
{1,,1{1◊2}2◊2} approximately corresponds to C(Ω₂+C(Ω₂2,0),C(Ω₂2,0))
{1,,1{1,,2◊2}2◊2} approximately corresponds to C(Ω₂+C(Ω₂,C(Ω₂2,0)),C(Ω₂2,0))
{1,,1{1,,1,,2◊2}2◊2} approximately corresponds to C(Ω₂+C(Ω₂2,C(Ω₂2,0)),C(Ω₂2,0))
{1,,1{1,,1,,2◊2}1,2◊2} approximately corresponds to C(Ω₂+C(Ω₂2,C(Ω₂2,0))+1,C(Ω₂2,0))
{1,,1,,2◊2} approximately corresponds to C(Ω₂+C(Ω₂,C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,0))
{1{1,,`1{1,,`1,2^,,}2^,,}2◊2} approximately corresponds to C(Ω₂+C(Ω₂+1,C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,0))
{1{1,,`1{1,,`1,,`2^,,}2^,,}2◊2} approximately corresponds to C(Ω₂+C(Ω₂2,C(Ω₂2,C(Ω₂2,0))),C(Ω₂2,0))
{1◊3} approximately corresponds to C(Ω₂2,C(Ω₂2,0))
{1◊1,2} approximately corresponds to C(Ω₂2+1,0)
{1{1{1,,`1{1◊1,2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} approximately corresponds to C(Ω₂+C(Ω₂2+C(Ω₂2+1,0),0),0)
{1{1{1,,`1{1◊1{1◊2}2}2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}2} approximately corresponds to C(Ω₂+C(Ω₂2+C(Ω₂2+C(Ω₂2,0),0),0),0)

31 thoughts on “sDAN vs. Taranovsky’s ordinal notation”

Aarex Tiaokhiao says:

So the limit of “…,, is C(C(Ω_2*2+C(Ω_2+C(C(Ω_2+1,C(Ω_2*2,0)),C(Ω_2,C(Ω_2*2,0))),0),0),0)

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2017-02-19 at 22:21
Aarex Tiaokhiao says:

And the limit of C(C(Ω_2*2+C(Ω_2+C(C(Ω_2*2+C(Ω_2+C(C(…),C(Ω_2,C(Ω_2,C(Ω_2*2)))))),C(Ω_2,C(Ω_2,C(Ω_2*2))))))) is approx {1{1{1,,,3}1{1{1{1,,,3}1{1{1,,,3}3}2,,,2}2{1,,,3}2}1{1,,,2}2{1{1,,,3}3}2,,,2}2,,,2}.

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2017-03-04 at 01:40
Boboris02 says:

What is the fixed point of α in C(C(Ω_2*2,α),0)?
Isn’t C(C(Ω_2+1,0),0) equal to the limit of C(C(Ω_2,C(Ω_2,C(Ω_2,C(Ω_2,……)))),0)?

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2017-03-27 at 00:18
- Boboris02 says:
  
  And doesn’t the same apply to C(C(Ω_2*2+1,0),0)
  
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  2017-03-27 at 00:20
- Aarex Tiaokhiao says:
  
  It is C(C(Ω_2*2+1,0),0) = C(C(C(0,C(Ω_2,Ω_2)),0),0).
  
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  2017-03-27 at 00:39
Boboris02 says:

Can you tell me how much is C(C(W_2*2+C(W_2*2,0),0),0) roughly in SAN?
I don’t find it.

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2017-03-28 at 01:12
- Aarex Tiaokhiao says:
  
  I guess he didn’t reach yet. He is at C(C(C(Ω_2,Ω_2)+C(Ω_2+C(Ω_2,C(C(Ω_2,Ω_2),C(C(Ω_2,Ω_2)))),0)+C(Ω_2+C(C(Ω_2,Ω_2),C(C(Ω_2,Ω_2))),0),0),0) for now.
  
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  2017-03-28 at 02:49
  - Boboris02 says:
    
    Do you have any guesses?
    
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    2017-03-29 at 02:00
    - Aarex Tiaokhiao says:
      
      I don’t know.
      
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      2017-03-29 at 07:13
Alemagno12 says:

According to my approximation method, C(C(Ω_2*3,0),0) = {1,,`1{1,,`1,,`2^,,}3^,,}

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2017-09-18 at 08:32
- hypcos says:
  
  What corresponds to {1{1,,`1,,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,} in your analysis?
  
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  2017-09-19 at 08:30
  - Aarex Tiaokhiao says:
    
    His approximation doesn’t work beyond {1{1{1{1,,’1,,2^,,}2^,,}2}2}.
    
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    2017-09-21 at 09:35
  - Alemagno12 says:
    
    According to my approximation method, C(Ω_2*2+C(Ω_2,C(Ω_2*2,0)),0)C(Ω_2+C(Ω_2,C(Ω_2*2,0)),C(Ω_2*2,0)) approximately corresponds to {1{1,,`1,,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}
    
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    2017-09-21 at 10:12
Alemagno12 says:

”{1,,`2`,,2^,,} has recursion level C(C(Ω_2*2+C(Ω_2+C(C(Ω_2*2,σ)+,σ+),0),0),0)
{1,,`1{1,,`2`,,2^,,}1`,,2^,,} has recursion level C(C(Ω_2*2+C(Ω_2+C(C(Ω_2+C(C(Ω_2*2,σ)+,σ+),C(Ω_2*2,σ)),σ+),0),0),0)
{1,,`1`,,3^,,} has recursion level C(C(Ω_2*2+C(Ω_2+C(C(Ω_2*2,C(Ω_2*2,σ)),σ+),0),0),0)”
Your analysis is wrong.

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2017-09-23 at 10:01
- hypcos says:
  
  Then what’s your comparisons of these 3 separators?
  
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  2017-09-23 at 21:44
- Alemagno12 says:
  
  Sorry for late reply.
  {1,,`2`,,2^,,} has recursion level C(C(Ω_2*2+C(Ω_2+C(C(Ω_2+σ++,σ),σ+),0),0),0)
  {1,,`3`,,2^,,} has recursion level C(C(Ω_2*2+C(Ω_2+C(C(Ω_2+σ++,C(Ω_2+σ++,σ)),σ+),0),0),0)
  
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  2017-10-07 at 09:37
  - Alemagno12 says:
    
    And {1,,`1{1,,`2`,,2^,,}2`,,2^,,} has recursion level
    
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    2017-10-07 at 09:40
    - Alemagno12 says:
      
      Umm, I can’t put the ordinal in my reply because else it will not send
      
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      2017-10-07 at 09:42
- hypcos says:
  
  But your C(Ω_2+C(C(Ω_2+σ++,σ),σ+),0) is not valid. Ω_2+C(C(Ω_2+σ++,σ),σ+) is not 2-built from below from <C(Ω_2+C(C(Ω_2+σ++,σ),σ+),0), because it contains a larger Ω_2+σ++, which is not 1-built from below from <C(Ω_2+C(C(Ω_2+σ++,σ),σ+),0), because it contains a larger Ω_2*2, which is not 0-built from below from <C(Ω_2+C(C(Ω_2+σ++,σ),σ+),0).
  
  Note that σ = C(Ω_2*2,0), σ+ = C(Ω_2,C(Ω_2*2,0)) and σ++ = C(Ω_2,C(Ω_2,C(Ω_2*2,0))).
  
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  2017-10-07 at 18:17
  - Alemagno12 says:
    
    Oh.
    
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    2017-10-20 at 10:28
Boboris02 says:

Is C(Ω_2*2+C(Ω_2+C(Ω_2*2+C(Ω_2*2,0),0),0),0) a valid term?

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2018-01-25 at 02:51
- hypcos says:
  
  Yes.
  
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  2018-01-25 at 08:01
  - Boboris02 says:
    
    In your analysis you go from C(C(Ω_2*2+C(Ω_2+C(Ω_2*2+C(Ω_2+C(Ω_2*2+1,0),0),0),0),0),0) directly to C(C(Ω_2*2+C(Ω_2*2,0),0),0), which would imply that the limit of:
    C(Ω_2*2,0),
    C(Ω_2*2+C(Ω_2+C(Ω_2*2,0),0),0),
    C(Ω_2*2+C(Ω_2+C(Ω_2*2+C(Ω_2+C(Ω_2*2,0),0),0),0),0),
    ect. is C(Ω_2*2+C(Ω_2*2,0),0) rather than C(Ω_2*2+C(Ω_2+C(Ω_2*2+C(Ω_2*2,0),0),0),0).
    So which one is it?
    
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    2018-01-27 at 21:34
    - hypcos says:
      
      C(C(Ω_2*2+C(Ω_2+C(Ω_2*2+C(Ω_2*2,0),0),0),0),0) is not a valid term.
      
      Let a(1) = C(Ω_2*2,0), a(n+1) = C(Ω_2+C(Ω_2*2+a(n),0),0). Then the limit of a(n) is C(Ω_2*2+C(Ω_2+C(Ω_2*2+C(Ω_2*2,0),0),0),0); but the limit of C(a(n),0) is C(C(Ω_2*2+C(Ω_2*2,0),0),0).
      
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      2018-01-28 at 08:12
Dessa Hall says:

Big hoss = s(100 100{1,,1,,2}2)
Same as s(100 100{1,,1,,1{1,,1,,2}2}2)

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2023-09-02 at 17:34
danieljr says:

So if {1{1{1,,`1,,2^,,}2,,`1{1,,`1{1,,`1,,`2^,,}2^,,}1,,2{1,,`1,,`2^,,}2^,,}1,,2} has recursion level C(C(Ω_2*3,0),0) in taranovsky’s ordinal notation, What would the recursion level be for {1{1{1,,,1,2}2}2}?

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2024-02-21 at 10:37
barrianic says:

{1`2{1`,,2^,,}2} has the same recursion level as {1{1{1`2{1`,,2^,,}2}2}2{1`,,2^,,}2} correct?

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2024-03-23 at 07:00
- barrianic says:
  
  I made a new account so I could create my own site
  
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  2024-04-18 at 09:08
  - barrianic says:
    
    oh, I did not
    
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    2024-04-18 at 09:09
    - barrianic says:
      
      nvm
      
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      2024-04-18 at 09:31
danieljr says:

{1{1{1,,`1{1,,`1,,`2^,,}3^,,}2}2} has recursion level C(C(Ω_2*3,0)+C(Ω_2+C(Ω_2*3,0)+C(Ω_2,C(Ω_2,C(Ω_2*2,0))),0),0)

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2024-04-03 at 02:04

Steps Toward Infinity!

A website on large numbers and fast-growing functions

sDAN vs. Taranovsky’s ordinal notation

Up to {1,,`1,,`2^,,}

Up to a C(Ω₂,C(Ω₂,C(Ω₂2,0)))

Up to a C(Ω₂,C(Ω₂,C(Ω₂,C(Ω₂2,0))))

Up to a C(Ω₂+C(Ω₂2,0),C(Ω₂2,0))

Beyond C(Ω₂+C(Ω₂2,0),C(Ω₂2,0))

Up to {1,,`1{1,,`1,,`2^,,}3^,,}

Up to a C(Ω₂,C(Ω₂2,C(Ω₂2,0)))

Up to a C(Ω₂2,C(Ω₂2,C(Ω₂2,0)))

Up to a C(Ω₂2+C(Ω₂2,0),0)

Beyond C(Ω₂2+C(Ω₂2,0),0)

31 thoughts on “sDAN vs. Taranovsky’s ordinal notation”

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Up to {1,,`1,,`2,,}

Up to a C(Ω2,C(Ω2,C(Ω22,0)))

Up to a C(Ω2,C(Ω2,C(Ω2,C(Ω22,0))))

Up to a C(Ω2+C(Ω22,0),C(Ω22,0))

Beyond C(Ω2+C(Ω22,0),C(Ω22,0))

Up to {1,,`1{1,,`1,,`2,,}3,,}

Up to a C(Ω2,C(Ω22,C(Ω22,0)))

Up to a C(Ω22,C(Ω22,C(Ω22,0)))

Up to a C(Ω22+C(Ω22,0),0)

Beyond C(Ω22+C(Ω22,0),0)

31 thoughts on “sDAN vs. Taranovsky’s ordinal notation”

. Cancel reply

Up to {1,,`1,,`2^,,}

Up to a C(Ω₂,C(Ω₂,C(Ω₂2,0)))

Up to a C(Ω₂,C(Ω₂,C(Ω₂,C(Ω₂2,0))))

Up to a C(Ω₂+C(Ω₂2,0),C(Ω₂2,0))

Beyond C(Ω₂+C(Ω₂2,0),C(Ω₂2,0))

Up to {1,,`1{1,,`1,,`2^,,}3^,,}

Up to a C(Ω₂,C(Ω₂2,C(Ω₂2,0)))

Up to a C(Ω₂2,C(Ω₂2,C(Ω₂2,0)))

Up to a C(Ω₂2+C(Ω₂2,0),0)

Beyond C(Ω₂2+C(Ω₂2,0),0)