User blog comment:B1mb0w/Growth Rate of the S Function/@comment-5529393-20160712123611/@comment-10262436-20160712124847

To specially answer your question.

S(S(n,T(0),1),T(0),1) reduces to S(S(n,T(0),1),S(n,T(0),1),1)

S(n,T(0),1) is a restricted S functions and so it is a valid 'a' parameter to substitute for T(0)