Definition of f(a,b,c)

F is a triadic/diadic/unacid/whatever function. 

First, trailing ,1's are removed. That is, f(a,1,1)=f(a,1)=f(a).

Next, f(a) = a^a.

Now, f(a,b)=f(f(a,b-1),b-1). Also, f(1,b)=f(b-1,b-1)=f(f(b-1,b-2),b-2).

For the triadic version it's a little different.

f(a,b,c)=f(f(a-1,b,c),f(a-1,b,c),c-1)

f(1,b,c)=f(f(b-1,b-1,c),b-1,c)

f(1,1,c)=f(f(c-1,c-1,c-1),f(c-1,c-1,c-1),c-1)