I built a dependency graph for Ackermann. Don't know if it helps.
╔═════╦═════╦═════╦═════╗
║ m= ║ 1 ║ 2 ║ 3 ║
╠═════╬═════╬═════╬═════╣
║ n=0 ║ 2 ║ ║ ║
╚═════╬══v══╣ ║ ║
║ 3 > 3 ║ ║
╠══v══╬══v══╣ ║
║ 4 ║ ║ ║
╠══v══╣ ║ ║
║ 5 > 5 > 5 ║
╠══v══╬══v══╬══v══╣
║ 6 ║ ║ ║
╠══v══╣ ║ ║
║ 7 > 7 ║ ║
╠══v══╬══v══╣ ║
║ 8 ║ ║ ║
╠══v══╣ ║ ║
║ 9 > 9 ║ ║
╠══v══╬══v══╣ ║
║ 10 ║ ║ ║
╠══v══╣ ║ ║
║ 11 > 11 ║ ║
╠══v══╬══v══╣ ║
║ 12 ║ ║ ║
╠══v══╣ ║ ║
║ 13 > 13 > 13 ║
╠══v══╬══v══╬══v══╣
║ 14 ║ ║ ║
╠══v══╣ ║ ║
║ 15 > 15 ║ ║
╠══v══╬══v══╣ ║
║ 16 ║ ║ ║
╠══v══╣ ║ ║
║ 17 > 17 ║ ║
╠══v══╬══v══╣ ║
║ 18 ║ ║ ║
╠══v══╣ ║ ║
║ 19 > 19 ║ ║
╠══v══╬══v══╣ ║
║ 20 ║ ║ ║
╠══v══╣ ║ ║
║ 21 > 21 ║ ║
╠══v══╬══v══╣ ║
║ 22 ║ ║ ║
╠══v══╣ ║ ║
║ 23 > 23 ║ ║
╠══v══╬══v══╣ ║
║ 24 ║ ║ ║
╠══v══╣ ║ ║
║ 25 > 25 ║ ║
╠══v══╬══v══╣ ║
║ 26 ║ ║ ║
╠══v══╣ ║ ║
║ 27 > 27 ║ ║
╠══v══╬══v══╣ ║
║ 28 ║ ║ ║
╠══v══╣ ║ ║
║ 29 > 29 > 29 ║
╚═════╩═════╩═════╝
Each box along the vertical axis is one "n" higher, so A(3,2)=A(2,13)=A(1,27)=29.
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