WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: goal(xs,ys) -> merge(xs,ys) merge(Cons(x,xs),Nil()) -> Cons(x,xs) merge(Cons(x',xs'),Cons(x,xs)) -> merge[Ite](<=(x',x),Cons(x',xs'),Cons(x,xs)) merge(Nil(),ys) -> ys - Weak TRS: <=(0(),y) -> True() <=(S(x),0()) -> False() <=(S(x),S(y)) -> <=(x,y) merge[Ite](False(),xs',Cons(x,xs)) -> Cons(x,merge(xs',xs)) merge[Ite](True(),Cons(x,xs),ys) -> Cons(x,merge(xs,ys)) - Signature: {<=/2,goal/2,merge/2,merge[Ite]/3} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {<=,goal,merge,merge[Ite]} and constructors {0,Cons,False ,Nil,S,True} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(0) <= :: ["A"(0) x "A"(0)] -(0)-> "A"(15) Cons :: ["A"(8) x "A"(8)] -(8)-> "A"(8) Cons :: ["A"(6) x "A"(6)] -(6)-> "A"(6) Cons :: ["A"(7) x "A"(7)] -(7)-> "A"(7) Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) False :: [] -(0)-> "A"(7) False :: [] -(0)-> "A"(15) Nil :: [] -(0)-> "A"(6) Nil :: [] -(0)-> "A"(8) S :: ["A"(0)] -(0)-> "A"(0) True :: [] -(0)-> "A"(7) True :: [] -(0)-> "A"(15) goal :: ["A"(14) x "A"(8)] -(16)-> "A"(0) merge :: ["A"(8) x "A"(6)] -(5)-> "A"(0) merge[Ite] :: ["A"(7) x "A"(8) x "A"(6)] -(0)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1) "Cons_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "False_A" :: [] -(0)-> "A"(1) "Nil_A" :: [] -(0)-> "A"(1) "S_A" :: ["A"(1)] -(1)-> "A"(1) "True_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))