User blog comment:Alemagno12/Divine Presence/@comment-24920136-20170201004922/@comment-30754445-20170201101424

Ah, Barry's Paradox.

But no, it doesn't apply here, because UHN itself cannot be represented as a Unicode String in UHN (and even if it did, the problem won't occur at A(6) because "R(X,1) where X is the definition for UHN" isn't the same as "R(X,1)")

I'm still not sure how the system works exactly. The paragraph describing how you create a "ruleset" or count the characters in that ruleset is unclear. It's clear what Alemagno tried to do, though: R does recursion and C does some kind of diagonalization. Not sure what RO is doing, but it looks like an attempt to create fundamental sequences automatically.

At any rate, once the final step is defined properly, I doubt it would be anything as strong as Rayo or FOOT. At best, it would be equivalent to a Turing-complete computer language, so A(n) ~ BB(n). And more likely, it would be a computable function with a pretty low ordinal (the exact ordinal depends on how complex a nesting we could squeeze out of C and RO)