User blog comment:B1mb0w/Rule 2B/@comment-5529393-20160207015116/@comment-5529393-20160218023424

In fact, answer A is correct; it is the correct application of the rule with beta = phi(2,0) + 1.

To see that answer B is different, remember that the function f(x) = phi(1,x) is an increasing function of x, so that phi(1,phi(2,0)+2) = phi(1,phi(1,phi(2,0)+1)+1) if and only if phi(2,0)+1 = phi(1,phi(2,0)+1). But the latter expression is the limit of w^(phi(2,0)+1), w^w^(phi(2,0)+1), w^w^w^(phi(2,0)+1), etc. Even w^(phi(2,0)+1) = phi(2,0) * w is clearly greater than phi(2,0) + 1.