User blog comment:TheMostAwesomer/Compressed BEAF: My own direction/@comment-27173506-20160124174647

The "Going Deeper" makes sense to me (Hyperlevel 1 is about f_w^w^w(n) if I'm not mistaken), the first section is weird.

The analysis is based on the fact that if a notation has level f_a(n), then a notation with the same rules but with the base rule changed to the limit of the old notation (the function on level f_a(n)), the new notation will have level f_a2(n).

Superlevel 0~f_w^w(n)

Superlevel 1~f_(w^w)2(n)

Superlevel n~f_(w^w)*(1+n) (n)

Duperlevel 0~f_w^w(n)

Duperlevel 1~f_(w^w)*w(n)=f_w^(w+1)(n)

Duperlevel n~f_(w^w)^n(n)

Truperlevel 1~f_w^(w*w) (n)=f_w^w^2(n)

Truperlevel n~f_w^((w^2)*n) (n)

Quadruperlevel 1~f_w^w^3(n)

1+nlevel 1~f_w^w^n(n)

Hyperlevel 1~f_w^w^w(n)