User blog comment:B1mb0w/Deeply Nested Ackermann/@comment-25337554-20150531035104/@comment-10262436-20150602105406

Hi again.

I calculated the growth rate and d(a, b) >> fa (b) in all cases, except for ridiculous cases where maybe b >> >> a.

d(x, y, z) doesn't grow as fast as w+1. When we compare growth rates to Graham's number, I get:

fw+1 (64) >> fw^64 (6) >> G

d(6,1,1,1, ... ,1,0) >> G where d has 64 input parameters. So the d function can grow at w+1 but only if we keep increasing the input parameters.

d(x, y, z) grows much faster than d(x, y) but still at about w only.