It looks nice. You can't change my mind.[]
function:
Define a!b as \(a\uparrow^{b}a-1\uparrow^{b}\cdots 2\uparrow^{b}1\)
a![1,b] = a!b
a![n,b] = (a!b)!b)!b)...!b) with n !b's for n> 1
a![1,m,b] = a![m,b]
a![m,1,b] = a![m,b]
a![m,b,1] = a![m,b]
a![m,1,1] = a!m
a![n,m,b] = a![n-1,\(f(m),f(b)\)] , \(f(n) = n![n-1,n,n]\)
It's kind big??
3![3,3,3] = 3![2,3![2,3,3],3![2,3,3]]
3![2,3,3] = 3![1,3![1,3,3],3![1,3,3]]
3![1,3,3] = ((3!3)!3)!3
3!3 = \(3\uparrow^32\uparrow^{3}1\)
and so on.