User blog comment:Boboris02/MBOT/@comment-30167082-20161218151736/@comment-30754445-20161219165557

Why do you think it would be uncomputable?

As long as Phi Systems can:

(1) Add, Subtract and compare numbers and variables

(2) Say stuff like "if X then Y"

(3) Do some kind branching (if X=0 go here, otherwise go there)

They can model any computer porgram and therefore any Turing Machine.

And these 3 conditions are really very basic stuff I would expect from even the simplest of formal languages. So yes, NOOP would almost definitely turn out to be uncomputable (and probably closer to BB-level then FOOT-level).

By the way, using the trick of "the largest number describable with n symbols in system X" to create a decent computable function is very difficult. Most systems are either too weak (resulting in a disappointing growth rate) or it is too strong (allowing Busy Beavers). For an impressive example of such a computable function, see "Loader's Number".