User blog comment:B1mb0w/Growth Rate of the S Function/@comment-25601061-20160708203814/@comment-10262436-20160711091153

Thanks for your calculations, however:

S(T(0),2,S(T(0),2,1)) is illegal according to the definitions because S(T(0),2,T(0))=S(T(0),3,1)

and so are

S(T(0),2,S(T(0),1,S(T(0),1,2)))

S(T(0),2,S(T(0),2,2))

S(T(0),2,S(T(0),2,3)

S(T(0),3,S(T(0),1,1))

 S(T(0),3,S(T(0),2,1))

S(T(0),3,S(T(0),3,1))

These results are similar to mine:

S(T(0),3,2)=e_e_0

S(T(0),3,T(0))=z_0  where  S(T(0),3,T(0))=S (T(0),4,1)

S(T(0),4,T(0))=n_0  where  S(T(0),4,T(0))=S (T(0),5,1)

 But this result looks slightly off

S(T(0),n,T(0))=phi(n,0)

I get

S(T(0),n,T(0))= S(T(0),n+1,1)== phi(n-1,0)

I'm not really sure about T(1) ... T(1) grows at just under phi(w,0)

f_ phi(w,0)(n) >>  S(n,T(1),1) = S(n,S(T(0),T(0),1),1) =  S(n,S(T(0),n,1),1) >> f_ phi(n-2,0)(n)