User blog comment:Mh314159/A hopefully powerful new system/@comment-35470197-20190628050713

I guess that '' in Rule set o for n sets of expressions is converted to an unintended font-assignment.

If I am correct, [n][n,…,n] is approximated by ω^2 in FGH, and [n,…,n][n,…,n] is bounded by ω^ω in FGH, [n,…,n]…[n,…,n] is bounded by ω^ω^2 in FGH. Although I have note read definitions containing backslashes, I guess from the pattern of your preference of recursion that the full notation will be bounded by ε_0 in FGH. Scaled in my googolgical ruler, ω^2 in FGH is of level 7, ω^ω in FGH is of level 8, and ε_0 in FGH is of level 10, while TREE(3) is of level greater than or equal to 13.

In order to create a stronger notation, you need to consider the way to invent shorter definitions. Otherwise, you will need hundreds of rule sets with hundreds of new symbols.