WORST_CASE(?,O(n^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: gcd(x,0()) -> x gcd(0(),y) -> y gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y))) - Signature: {gcd/2} / {-/2,0/0, [1] x + [0] = x gcd(0(),y) = [1] y + [11] > [1] y + [0] = y gcd(s(x),s(y)) = [10] x + [1] y + [1] > [0] = if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y))) Following rules are (at-least) weakly oriented: WORST_CASE(?,O(n^1))