Analysis

n(H) = n

length(rootlist) $\leq$ D(n) + t(H) - 1

T(while loop) $\leq$ D(n) + t(H)

c_i = O(D(n) + t(H))

= t(H) + 2m(H)

$\leq$ D(n) + 1 + 2m(H)

= c_i + (D(n) + 1 + 2m(H)) - (t(H) + 2m(H))

= O(D(n) + t(H)) + D(n) + 1 - t(H)

= O(D(n))

Assuming adjustment of potential coefficients to dominate coefficients hidden in O(t(H)).