WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: +Full(0(),y) -> y +Full(S(x),y) -> +Full(x,S(y)) f(x) -> *(x,x) goal(xs) -> map(xs) map(Cons(x,xs)) -> Cons(f(x),map(xs)) map(Nil()) -> Nil() - Weak TRS: *(x,0()) -> 0() *(x,S(0())) -> x *(x,S(S(y))) -> +(x,*(x,S(y))) *(0(),y) -> 0() - Signature: {*/2,+Full/2,f/1,goal/1,map/1} / {+/2,0/0,Cons/2,Nil/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {*,+Full,f,goal,map} and constructors {+,0,Cons,Nil,S} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- * :: ["A"(1) x "A"(7)] -(7)-> "A"(1) + :: ["A"(0) x "A"(0)] -(3)-> "A"(3) +Full :: ["A"(10) x "A"(0)] -(8)-> "A"(0) 0 :: [] -(0)-> "A"(10) 0 :: [] -(0)-> "A"(7) 0 :: [] -(0)-> "A"(1) Cons :: ["A"(12) x "A"(12)] -(12)-> "A"(12) Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) Nil :: [] -(0)-> "A"(12) Nil :: [] -(0)-> "A"(6) S :: ["A"(10)] -(10)-> "A"(10) S :: ["A"(7)] -(7)-> "A"(7) S :: ["A"(0)] -(0)-> "A"(0) f :: ["A"(9)] -(9)-> "A"(1) goal :: ["A"(14)] -(8)-> "A"(0) map :: ["A"(12)] -(6)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "+_A" :: ["A"(0) x "A"(0)] -(0)-> "A"(0) "0_A" :: [] -(0)-> "A"(1) "Cons_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "Nil_A" :: [] -(0)-> "A"(1) "S_A" :: ["A"(1)] -(1)-> "A"(1) WORST_CASE(?,O(n^1))