User:Wythagoras/Rado's sigma function/BB(38)

\(\Sigma(42) > f_{\omega2}(167)\) 0 _ 1 l bb1 0 1 _ r bb2 bb1 _ 1 l bb2 bb1 1 1 l bb3 bb2 _ 1 r 0 bb2 1 _ l bb1 bb3 _ _ l bb4 bb3 1 _ l 18 bb4 _ 1 r bb2 bb4 1 1 l 0 1 1 1 l 1 1 _ 1 r 2 2 1 1 r 2 2 _ _ r 3 3 _ _ r 14 3 1 1 r 4 4 1 1 l 5 4 _ _ r 6 5 1 _ l 5 5 _ 1 l 1 6 _ _ r 14 6 1 1 r 7 7 _ _ r 6 7 1 1 l 8 8 1 _ l 9 8 _ 1 l 17 9 _ _ l 10 9 1 1 r 11 10 1 1 l 9 10 _ 1 r 1 11 1 _ r 12 11 _ _ l 13 12 _ 1 r 11 12 1 1 l 13 13 1 1 l 13 13 _ 1 l 10 14 _ _ r halt 14 1 1 r 15 15 _ _ r 20 15 1 1 l 16 16 1 _ l 16 16 _ _ l 8 17 1 1 l 18 17 _ 1 l 1 18 _ _ l 19 18 1 _ l 19 19 1 1 l 18 19 _ 1 l 1 20 _ _ r halt 20 1 1 r 21 21 _ _ r 20 21 1 1 l 22 22 1 _ l 22 22 _ 1 l 23 23 1 1 l 35 23 _ 1 r 24 24 _ 1 l 25 24 1 1 r 31 25 1 1 l 25 25 _ 1 l 26 26 1 1 l 25 26 _ _ l 27 27 _ _ l 28 27 1 _ r 30 28 _ 1 r 29 28 1 1 r 27 29 _ _ r 29 29 1 1 r 30 30 1 1 r 30 30 _ 1 r 24 31 _ _ l 32 31 1 1 l 33 32 1 1 l 32 32 _ _ r 28 33 1 1 l 34 34 1 1 l 34 34 _ _ r 35 35 1 1 r 36 35 _ _ l 23 36 1 _ l 37 36 _ _ l 37 37 1 1 l 36 37 _ _ l 1

Explanation
This second part machine outputs more than \(f_{\omega2}(n)\) 1's if \(1\_\_(1\_)^n11\) is entered, and the second part uses Deedlit11's machine. The first part is a machine for \(\Sigma(5)\).