WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: even(Cons(x,Nil())) -> False() even(Cons(x',Cons(x,xs))) -> even(xs) even(Nil()) -> True() goal(x,y) -> and(lte(x,y),even(x)) lte(Cons(x,xs),Nil()) -> False() lte(Cons(x',xs'),Cons(x,xs)) -> lte(xs',xs) lte(Nil(),y) -> True() notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() - Weak TRS: and(False(),False()) -> False() and(False(),True()) -> False() and(True(),False()) -> False() and(True(),True()) -> True() - Signature: {and/2,even/1,goal/2,lte/2,notEmpty/1} / {Cons/2,False/0,Nil/0,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {and,even,goal,lte,notEmpty} and constructors {Cons,False ,Nil,True} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- Cons :: ["A"(1) x "A"(1)] -(1)-> "A"(1) Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) Cons :: ["A"(4) x "A"(4)] -(4)-> "A"(4) False :: [] -(0)-> "A"(0) Nil :: [] -(0)-> "A"(1) Nil :: [] -(0)-> "A"(4) Nil :: [] -(0)-> "A"(0) True :: [] -(0)-> "A"(0) and :: ["A"(0) x "A"(0)] -(0)-> "A"(0) even :: ["A"(1)] -(5)-> "A"(0) goal :: ["A"(8) x "A"(14)] -(16)-> "A"(0) lte :: ["A"(0) x "A"(4)] -(3)-> "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) WORST_CASE(?,O(n^1))