WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(+(x,y)) -> *(f(x),f(y)) f(+(x,s(0()))) -> +(s(s(0())),f(x)) f(0()) -> s(0()) f(s(0())) -> *(s(s(0())),f(0())) f(s(0())) -> s(s(0())) - Signature: {f/1} / {*/2,+/2,0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {*,+,0,s} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- * :: ["A"(0) x "A"(0)] -(0)-> "A"(5) * :: ["A"(0) x "A"(0)] -(0)-> "A"(7) + :: ["A"(4) x "A"(4)] -(4)-> "A"(4) + :: ["A"(0) x "A"(0)] -(0)-> "A"(0) 0 :: [] -(0)-> "A"(4) 0 :: [] -(0)-> "A"(13) 0 :: [] -(0)-> "A"(15) 0 :: [] -(0)-> "A"(14) f :: ["A"(4)] -(1)-> "A"(0) s :: ["A"(4)] -(4)-> "A"(4) s :: ["A"(0)] -(0)-> "A"(0) s :: ["A"(1)] -(1)-> "A"(1) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "*_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(0) "+_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(0) "0_A" :: [] -(0)-> "A"(1) "s_A" :: ["A"(1)] -(1)-> "A"(1) WORST_CASE(?,O(n^1))