WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) f(0()) -> 1() f(s(x)) -> g(x,s(x)) g(0(),y) -> y g(s(x),y) -> g(x,+(y,s(x))) g(s(x),y) -> g(x,s(+(y,x))) - Signature: {+/2,f/1,g/2} / {0/0,1/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,f,g} and constructors {0,1,s} + Applied Processor: Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing} + Details: Signatures used: ---------------- + :: ["A"(0, 0) x "A"(1, 0)] -(1)-> "A"(0, 0) 0 :: [] -(0)-> "A"(1, 0) 0 :: [] -(0)-> "A"(2, 1) 0 :: [] -(0)-> "A"(3, 1) 1 :: [] -(0)-> "A"(0, 0) f :: ["A"(2, 1)] -(1)-> "A"(0, 0) g :: ["A"(3, 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"(4, 1)] -(3)-> "A"(3, 1) s :: ["A"(0, 0)] -(0)-> "A"(0, 0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(0) "1_A" :: [] -(0)-> "A"(0) "s_A" :: ["A"(0)] -(0)-> "A"(0) WORST_CASE(?,O(n^2))