User blog comment:B1mb0w/Strong D Function Calculations/@comment-1605058-20150630143353/@comment-25337554-20150701103017

w+2 is much larger than left side.

$$f_{\omega+2}(n)=f_{\omega+1}^n (n)=f_{\omega+1}^{n-1} (f_{\omega+1} n)=f_{\omega+1}^{n-1} (f_{\omega}^n n)=f_{\omega+1}^{n-2} (f_{\omega+1}(f_{\omega}^n n))>f_{\omega+1}^{n-2} (f_{\omega}^{n\uparrow\uparrow n}(n))$$