User blog comment:Primussupremus/More ideas for my notation./@comment-73.235.194.108-20170427144325

You should give more examples. How exactly does the incrementer work? (a,b,c#[x]|{y}) is defined I guess but what about (a,b,c#[x]|{y}|{k})? Here is my idea.

(a,b,c#[x]|{1}|{1}) =  (a,b,c)

(a,b,c#[x]|{y}|{1}) = (a,b,c#[x]]|{(a,b,c#[x]|[y-1]|{1})}|{1})

This is the sort of recursion that you have been doing so you can continue it.

(a,b,c#[x]|{1}|{k}) =  (a,b,c)

 (a,b,c#[x]|{y}|{k}) = (a,b,c#[x]]|{(a,b,c#[x]|[y-1]|{k})}|{k-1})

 That will acheive w2 growth rate.