User blog:Username5243/Extended Up-arrow Notation

This is another notation from the xkcd games.

Definition
a^1b = a^b a^c+1,d,...b = a^c,d,...a^c+1,d,...b-1 a^...1 = a a^1,1,...,1,1,c,...b = a^1,1,...,1,b,c-1,...a

That's all for now. I believe this notation reaches w^w level so far.