User blog comment:B1mb0w/Growth Rate of the S Function/@comment-5529393-20160712123611/@comment-10262436-20160712130442

I allowed for this. All S functions can have b=0 and c=0. This is in the defining rules. However c>0 if b>0 to avoid errors.

Therefore T(0) is equal to the generalised S function S(T(0),0,0) = T(0). This is stated in the rule S(a,b,0)=a for any b.