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