Type the master-theorem three-way comparison, in words

Answer

W = n^(log_b a) # watershed = #leaves f smaller than W (poly) -> case 1 -> Theta(W) f equal to W (x lg^k n) -> case 2 -> Theta(W lg^{k+1} n) f bigger than W (poly)+reg -> case 3 -> Theta(f)

Every classification is one question — is f polynomially below, equal to, or polynomially above the watershed n^(log_b a)? Case 2 (the tie) tacks on exactly one extra log per lg^k factor in f.