User blog comment:Mh314159/new YIP notation/@comment-39585023-20190714235606/@comment-39585023-20190718143227

"The rules "n=[a−1],[a]=gnn(n)" are a little confusing, because the dependency of these two variables are not declared."

[1] = g11(1) because [0] is 1 by definition. And [2] = gnn(n) where n = [1], etc. I think the rules work for all values of a greater than zero. So that Is that what I need to declare?

"Maybe the rule for Y should be placed after the rule for 0 0(x), because you use 0 0(x) only for the case where the first entry is positive."

I don't understand this one. In rule set two, we have the definition  0 0(x) = [x,x,...,x,β-1] with N terms; it converges because we are reducing the final term by one compared to the term we are recursing and there is a rule to drop zeroes so eventually the number of terms decreases. The rule for Y is used to reduce a string that has an initial zero, which can only happen when finding the value of n to substitute into gnn(n), not when applying  0 0(x). When an inital term reaches zero when defining n, then the last term decrements and the first term grows, creating many recursions but the process still converges. The "oscillation" between decrementing last term for  0 0(x) but first term for gnn(n) what what I was hoping would produce complex recursions.