User blog comment:Revilo30703/Knuth's Up Arrow Infinite Expantion/@comment-27173506-20160123125539/@comment-27659163-20160123182206

If you were to have 3^(3,2)4, it would equal 3^(3,1)(3^(3,1)(3^(3,1)3)), because you would try to reduce the lenght first.

The second step gives you  3^(3,1)(3^(3,1)(3^(2,3)(3^(2,3)3))) Reducing the height because the legnth is at one for the inermost parentheses.

Then you get  3^(3,1)(3^(3,1)(3^(2,3)(3^(2,2)(3^(2,2)3)))) again reducing the "legnth" of the inermost parentheses.

The third step:    3^(3,1)(3^(3,1)(3^(2,3)(3^(2,2)(3^(2,1)(3^(2,1)3))))) reducing legnth

3^(3,1)(3^(3,1)(3^(2,3)(3^(2,2)(3^(2,1)(3^(1,3)(3^(1,3)3)))))) reducing height

3^(3,1)(3^(3,1)(3^(2,3)(3^(2,2)(3^(2,1)(3^(1,3)27))))) simplifying, remember ^(3) is the same as normal exponentiation

3^(3,1)(3^(3,1)(3^(2,3)(3^(2,2)(3^(2,1)7625597484987 )))) More symplifying

At this point I'm going to stop because the numbers are to big to use, hopfuly you can see the patern from this.