User blog comment:Emlightened/Ordinals in Type Theory/@comment-11227630-20180128144447

A term a is λ→-typed if there exists such b that a:b in λ→. And let Λ(n) be the maximal length of beta-normal forms of λ→-typed terms with length ≤n (here, the "length" of a term is the total amount of varibles, including term varibles and type varibles). Then Λ(n) has tetration growth rate (more exactly, Λ(n) is comparable to 2↑↑(log(n))), which is not very high in googological sense.

Then what about the growth rates of such Λ functions defined on "λ→ with ×", "λ→ with Nat", "λ→ with Ord", and "λ→ with Nat with Ord"?