Do there exist two computable functions, a and b, which can construct every computable function by a finite serie of a's and b's which is function composed? Fx. let's take the serie, a,b,a,b,b,a,a,a , which function composed is the function, a∘b∘a∘b∘b∘a∘a∘a ( =a(b(a(b(b(a(a(a(x)))))))) ), this function is the function described by the serie, a,b,a,b,b,a,a,a. And I want to know if every program can be described, by such serie.
If such functions exist, can you tell a example of a and b?