User blog comment:Mh314159/Natural number recursion - first 4 rule sets/@comment-35470197-20191019143654/@comment-35470197-20191019144553

In addition, as I commented to the previous blog post, if you intend your function to be non-total, then it is better to clarify it. For example, it is good to clarify all conditions of expressions which you intend to apply the rulesby writing something like "I define an assignment of a natural number to each expression of the form A(x) or A^m(x), where A is the fixed function symbol, S is strings consisting of natural numbers in which at most one entry is 0, m is a natural number, and x is a natural number". Otherwise, it is reasonable for others to assume that you are considering a total function, i.e. you allow the case \(S = (0,1,0,1,0,1)\).