WORST_CASE(?,O(n^2)) Solution: --------- Cons :: [A(0, 12) x A(15, 12)] -(3)-> A(3, 12) Cons :: [A(0, 0) x A(12, 0)] -(12)-> A(12, 0) Cons :: [A(0, 0) x A(0, 0)] -(0)-> A(0, 0) Nil :: [] -(0)-> A(3, 12) Nil :: [] -(0)-> A(12, 0) Nil :: [] -(0)-> A(7, 6) S :: [] -(0)-> A(7, 13) add0 :: [A(12, 0) x A(0, 0)] -(1)-> A(0, 0) goal :: [A(13, 14) x A(15, 14)] -(12)-> A(0, 0) mul0 :: [A(3, 12) x A(1, 0)] -(1)-> A(0, 0) Cost Free Signatures: --------------------- Cons :: [A_cf(0, 0) x A_cf(12, 0)] -(12)-> A_cf(12, 0) Cons :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) Nil :: [] -(0)-> A_cf(12, 0) Nil :: [] -(0)-> A_cf(14, 2) Nil :: [] -(0)-> A_cf(0, 0) S :: [] -(0)-> A_cf(11, 11) S :: [] -(0)-> A_cf(0, 0) add0 :: [A_cf(12, 0) x A_cf(12, 0)] -(0)-> A_cf(12, 0) add0 :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) mul0 :: [A_cf(12, 0) x A_cf(0, 0)] -(0)-> A_cf(12, 0) Base Constructors: ------------------ Cons_A :: [A(0, 0) x A(1, 0)] -(1)-> A(1, 0) Cons_A :: [A(0, 1) x A(1, 1)] -(0)-> A(0, 1) Nil_A :: [] -(0)-> A(1, 0) Nil_A :: [] -(0)-> A(0, 1) S_A :: [] -(0)-> A(1, 0) S_A :: [] -(0)-> A(0, 1)