WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: add(0(),y) -> y add(s(x),y) -> s(add(x,y)) mult(0(),y) -> 0() mult(s(x),y) -> add(x,mult(x,y)) - Signature: {add/2,mult/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {add,mult} and constructors {0,s} + Applied Processor: Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(1, 0) 0 :: [] -(0)-> "A"(2, 1) 0 :: [] -(0)-> "A"(0, 0) add :: ["A"(1, 0) x "A"(0, 0)] -(1)-> "A"(0, 0) mult :: ["A"(2, 1) x "A"(0, 0)] -(1)-> "A"(0, 0) s :: ["A"(1, 0)] -(1)-> "A"(1, 0) s :: ["A"(3, 1)] -(2)-> "A"(2, 1) s :: ["A"(0, 0)] -(0)-> "A"(0, 0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(0) "s_A" :: ["A"(0)] -(0)-> "A"(0) WORST_CASE(?,O(n^2))