WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,Cons(x',xs)) -> f[Ite][False][Ite](lt0(x,Cons(Nil(),Nil())),x,Cons(x',xs)) f(x,Nil()) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil())))) g(x,Cons(x',xs)) -> g[Ite][False][Ite](lt0(x,Cons(Nil(),Nil())),x,Cons(x',xs)) g(x,Nil()) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil())))) goal(x,y) -> Cons(f(x,y),Cons(g(x,y),Nil())) lt0(x,Nil()) -> False() lt0(Cons(x',xs'),Cons(x,xs)) -> lt0(xs',xs) lt0(Nil(),Cons(x',xs)) -> True() notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() number4(n) -> Cons(Nil(),Cons(Nil(),Cons(Nil(),Cons(Nil(),Nil())))) - Weak TRS: f[Ite][False][Ite](False(),Cons(x,xs),y) -> f(xs,Cons(Cons(Nil(),Nil()),y)) f[Ite][False][Ite](True(),x',Cons(x,xs)) -> f(x',xs) g[Ite][False][Ite](False(),Cons(x,xs),y) -> g(xs,Cons(Cons(Nil(),Nil()),y)) g[Ite][False][Ite](True(),x',Cons(x,xs)) -> g(x',xs) - Signature: {f/2,f[Ite][False][Ite]/3,g/2,g[Ite][False][Ite]/3,goal/2,lt0/2,notEmpty/1,number4/1} / {Cons/2,False/0 ,Nil/0,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,f[Ite][False][Ite],g,g[Ite][False][Ite],goal,lt0 ,notEmpty,number4} and constructors {Cons,False,Nil,True} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- Cons :: ["A"(0) x "A"(3)] -(3)-> "A"(3) Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) Cons :: ["A"(0) x "A"(1)] -(1)-> "A"(1) Cons :: ["A"(0) x "A"(7)] -(7)-> "A"(7) Cons :: ["A"(0) x "A"(2)] -(2)-> "A"(2) Cons :: ["A"(0) x "A"(9)] -(9)-> "A"(9) False :: [] -(0)-> "A"(3) False :: [] -(0)-> "A"(15) Nil :: [] -(0)-> "A"(3) Nil :: [] -(0)-> "A"(1) Nil :: [] -(0)-> "A"(0) Nil :: [] -(0)-> "A"(7) Nil :: [] -(0)-> "A"(15) Nil :: [] -(0)-> "A"(13) Nil :: [] -(0)-> "A"(12) True :: [] -(0)-> "A"(3) True :: [] -(0)-> "A"(15) f :: ["A"(7) x "A"(3)] -(3)-> "A"(0) f[Ite][False][Ite] :: ["A"(3) x "A"(7) x "A"(3)] -(0)-> "A"(0) g :: ["A"(7) x "A"(3)] -(8)-> "A"(0) g[Ite][False][Ite] :: ["A"(3) x "A"(7) x "A"(3)] -(5)-> "A"(0) goal :: ["A"(14) x "A"(9)] -(16)-> "A"(0) lt0 :: ["A"(0) x "A"(1)] -(1)-> "A"(9) notEmpty :: ["A"(7)] -(9)-> "A"(0) number4 :: ["A"(0)] -(16)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "Cons_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1) "False_A" :: [] -(0)-> "A"(1) "Nil_A" :: [] -(0)-> "A"(1) "True_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))