User blog comment:Wythagoras/All my stuff/@comment-7484840-20130708083606

With the y function, if you are judging efficiency on number of rules alone, then I could probably make a variant on HAN that would get to phi(omega,0) with only 5 or so rules.

Also, the ordinals need a lot more rules. Even f_omega(n) needs 3, and then as soon as you start doing operations on the ordinals, that needs more rules about how fundamental sequences work.