User blog comment:Mh314159/Natural number recursion - first 4 rule sets/@comment-35470197-20191019143654/@comment-39585023-20191019150129

Excellent observation. It probably makes sense to iterate the function first and then apply zero replacement, so I would say that A⟨0,1⟩2(x)  should first iterate to A⟨0,1⟩(A⟨0,1⟩(x)) and then we do zero replacement from right to left. Do you agree that this makes the most sense? I have recursed it both ways using the drop drailing zeroes rule for the  A⟨A⟨1,0⟩2(x),0⟩2(x) expression and both of them recurse, but differently, and I think the "iterate first" expression came out larger.