User blog:Ubersketch/I need some help with this unnamed notation.

So the other day I posted this to reddit. https://www.reddit.com/r/googology/comments/9g5a1j/something_i_made/ I haven't well defined it, and I haven't even made any remotely formal rules. Here goes nothing. Only the first entry can be followed with a +. {a} {a+} = a+1 {a+[1]b} = {a+}+}...} with b pairs of braces. {a+[1]b[1]c} = {a+[1]b} c times (i.e. {a+[1]b[1]c} uses {a+[1]b} as the input for a c times) {a+[2]b} = {a+[1]a[1]a...} with a [1]s. @a = {a+[2]b} {a+[3]b} = {@...a} with b @ This goes on for a long (uotc) while. I'd love it if you guys pointed out and flaws, undefinedness, and left ideas for extensions. I suspect this function has the level of $$\epsilon_0$$