This is the turing machine code computing FGH of growth rate less than \(\omega\).
Use http://morphett.info/turing/turing.html to paste this program.
Input form: to represent \(f_{a_1}(f_{a_2}(f_{a_3}(f_{a_4}(...f_{a_x}(n)...))))\), type \(a_x+1\) "O"s, then \(a_{x-1}+1\) "O"s, \(a_{x-2}+1\) "O"s,... ,\(a_1+1\) "O"s, each strings have a space between it. Then "*|", and insert \(n\) "1"s after that.
Output \(m\) here is represented with "|" followed by \(m\) "1"
Turing machine code[]
0 | | l 1 1 _ _ l 1p 1p _ _ r 5 1p O O l 1 1 O O l 1 2 * * r 2 2 _ _ r 2p 2 O x r 6 2p * * r 2p 2p | | r 3 2 | | r 3 3 1 1 r 3 3 _ 1 l 4 4 * * l 4 4 | | * 0 5 * * r 5p 5p O _ r 2 5p | | * halt 6 O x r 6 6 _ _ r 6p 6 | | r 7 6p * * r 6p 6p | | r 7 7 * a r 7 7 | | r 7 7 y O r 7 7 _ _ l 8 7 b b l 8 8 a b l 9u 8 | | r 13 9u * * l 9u 9u O O * 9 9u x x * 9 9 * * l 9 9 u x l 9p 9p u x l 9p 9p _ _ r 9pp 9pp x x r 9pp 9pp * * l 9ppp 9ppp x y l 10 9 x y l 10 10 * * l 10 10 _ _ l 10p 10p _ u r 11 10p u u l 10p 11 * * r 11 11 | | l 12 12 y * l 12p 12 * * l 12 12 x y l 10 12p y * l 12p 12p x y l 10 12p _ _ r 12pp 12pp * * r 12pp 12pp y O r 12pp 12pp | | * 7 13 b 1 r 13 13 _ _ l 14 14 * * l 14 14 | | l 15 15 O O l 15 15 _ _ l 15p 15 x O l 15 15 u _ l 15 15p x O l 15 15p u _ l 15 15p O O l 15 15p _ _ r 16 16 * * r 16 16 | | * 0