User blog comment:B1mb0w/Growth Rate of the S Function/@comment-25601061-20160708203814/@comment-5529393-20160714133136

Hmm, upon further consideration I get

S(T(1),1,1) ~ phi(w,0)2 S(T(1),2,1) ~ phi(w,0)^2 S(T(1),2,T(0)) ~ phi(1,phi(w,0)+1) S(T(1),3,1) = S(T(1),2,T(1)) ~ phi(1,phi(w,0)*2) S(T(1),3,2) ~ phi(1,(phi(1,phi(w,0)*2)) S(T(1),3,T(0)) ~ phi(2,phi(w,0)+1) S(T(1),3,S(T(0),1,1)) ~ phi(2,phi(w,0)+2) S(T(1),3,S(T(0),2,1)) ~ phi(2,phi(w,0)+w) S(T(1),3,S(T(0),3,1)) ~ phi(2,phi(w,0)+phi(1,0)) S(T(1),4,1) = phi(T(1),3,T(1)) ~ phi(2,phi(w,0)*2) S(T(1),5,1) = phi(3,phi(w,0)*2) S(T(1),T(0),1) = phi(w,1)