User blog comment:B1mb0w/Strong D Function/@comment-25337554-20150702100740

Proof that D(1,9,9)&lt;G:

D(x,y)<f_{x}(y)

$$D(1,0,0)=D(4,4)<f_{4}4=f_{\omega}(4)$$

$$D(1,0,1)=D(D(1,0,0),D(1,0,0))<f_{f_{\omega}(4)}(4)=f_{\omaga}^2 (4)$$

$$D(1,9,9)=D(1,0,63)$$

Therefore,

$$D(1,9,9)<f_{\omaga}^64 (4) $$

By the way,

$$f_a (b)<2\uparrow^a b$$

$$f_4(4)-3\uparrow^4(3)$$

$$<2\uparrow^3 2\uparrow^3 4- 3\uparrow^3 3\uparrow^3 3 $$

$$=2\uparrow^3 2\uparrow^2 2\uparrow^2 4- 3\uparrow^3 3\uparrow^2 3\uparrow^2 3 $$

$$2\uparrow\uparrow4=65536<3\uparrow\uparrow3$$

Therefore, $$f_4(4)<3\uparrow^4 3$$

Therefore, D(1,9,9)&lt;G.

Is there any wrong point in this?