User:Wythagoras/Rado's sigma function/BB(14,4)

\(\Sigma(14,4) > f_{\omega+2}(3)\) 0 _ 3 r 6 0 3 3 l 6 0a _ 1 r 0a 0a 1 _ l 0a 0a 2 1 r 1 0a 3 1 l 11 1 3 1 l 11 1 1 2 l 3 1 2 2 r 2 1 _ _ r 12 2 _ _ r 12 2 2 2 r 2 2 1 _ l 8 2 3 1 l 11 3 2 1 l 3 3 1 1 l 3 3 _ 1 l 0a 4 2 1 l 9 4 1 1 l 4 4 _ 2 r 6 4 3 3 l 13 6 _ 3 l 0 6 1 1 r 6 6 2 2 * 4 6 3 _ l 4 7 1 1 l 7 7 2 2 l 7 7 _ 1 l 0a 8 2 2 l 8 8 1 1 r 4 8 _ 3 l 13 9 1 1 l 9 9 2 3 l 9 9 _ 2 r 10 10 _ 2 l 7 10 1 1 r 10 10 2 2 * 4 10 3 2 r 10 11 2 2 l 11 11 1 2 l 11 11 _ 2 l 7 12 _ 1 r halt 12 3 _ l 8 13 2 3 l 13 13 1 3 l 13 13 3 3 l 13 13 _ 3 l 7

Explanation
A modified machine for \(\Sigma(2,2)\) is hidden in the machine, in state 0 and 8. It outputs: 3_33 ^ It uses groups, the first group duplicates, the second group is comparable to \(2^n\), the third group is comparable to \(2\uparrow\uparrow n\), the fourth group is comparable to \(2\uparrow\uparrow\uparrow n\), etc. Then for each 3 all ones will be changed into two's, giving a function comparable to \(f_{\omega}(n)\). For each three after the space \(f_{\omega+1}(n)\) the content before the same space will be changed to threes.

It uses LittlePeng9's duplication machine.