S(r) = r
S(r,1,...) = r
S(r,a) = a^^...a^r arrows...^^a
S(1,a,b) = S(1,S(1,a),b-1)
S(r,a,b) = Ss(r-1,a,b)
S(r,a,b,1,1,...,1,1,c,...) = S(S(r,a,b),S(r,a,b),a,a...,a,a,S(r,a,b-1,...,1,c,...),c-1,...)
S(r,a,b,c,...) = S(r,S(r,a,b),S(r,S(r,a,b),b-1,c,...),c-1,...)

SS(f,r,a,b) = f(r,a,a,a,...b a's...,a,a,a)
SS(f,r,1,a,b) = SS(f,r,a,b)
SS(f,r,k,a,b) = SS(f,SS(f,SS(...(SS(f,r,k-1,a,b)...),k-1,a,b),k-1,a,b),k-1,a,b) with k ('s
SS(f,r,1,1...,1,1,k,...,a,b) = SS(f,r,r,...,r,SS(f,r-1,k,a,b),k-1,...,a,b)
SS(f,r,k,...,a,b) = SS(f,SS(f,SS(...(SS(f,r-1,k,...,a,b)...),k-1,...,a,b),k-1,...,a,b),k-1,...,a,b) with k ('s

S2(...) = SS(S,...)
S3(...) = SS(S2,...)
S4(...) = SS(S3,...)
Sn(...) = SS(Sn-1,...)