WORST_CASE(?,O(n^2)) Solution: --------- 0 :: [] -(0)-> A(0, 0) 0 :: [] -(0)-> A(1, 0) 0 :: [] -(0)-> A(5, 5) 0 :: [] -(0)-> A(1, 5) false :: [] -(0)-> A(9, 9) false :: [] -(0)-> A(15, 15) gcd :: [A(5, 5) x A(1, 5)] -(2)-> A(0, 0) if_gcd :: [A(9, 9) x A(2, 5) x A(1, 5)] -(2)-> A(0, 0) le :: [A(0, 0) x A(1, 0)] -(1)-> A(12, 12) minus :: [A(5, 5) x A(0, 0)] -(1)-> A(5, 5) s :: [A(0, 0)] -(0)-> A(0, 0) s :: [A(1, 0)] -(1)-> A(1, 0) s :: [A(10, 5)] -(5)-> A(5, 5) s :: [A(6, 5)] -(1)-> A(1, 5) s :: [A(7, 5)] -(2)-> A(2, 5) s :: [A(5, 0)] -(5)-> A(5, 0) true :: [] -(0)-> A(9, 9) true :: [] -(0)-> A(15, 15) Cost Free Signatures: --------------------- 0 :: [] -(0)-> A_cf(0, 0) false :: [] -(0)-> A_cf(0, 0) false :: [] -(0)-> A_cf(1, 1) false :: [] -(0)-> A_cf(3, 3) gcd :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) if_gcd :: [A_cf(1, 1) x A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) if_gcd :: [A_cf(0, 0) x A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) le :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) le :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(3, 3) minus :: [A_cf(5, 0) x A_cf(0, 0)] -(1)-> A_cf(0, 0) minus :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) s :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) s :: [A_cf(5, 0)] -(5)-> A_cf(5, 0) true :: [] -(0)-> A_cf(0, 0) true :: [] -(0)-> A_cf(1, 1) true :: [] -(0)-> A_cf(3, 3) Base Constructors: ------------------ 0_A :: [] -(0)-> A(1, 0) 0_A :: [] -(0)-> A(0, 1) false_A :: [] -(0)-> A(1, 0) false_A :: [] -(0)-> A(0, 1) s_A :: [A(1, 0)] -(1)-> A(1, 0) s_A :: [A(1, 1)] -(0)-> A(0, 1) true_A :: [] -(0)-> A(1, 0) true_A :: [] -(0)-> A(0, 1)