WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: addlist(Cons(x,xs'),Cons(S(0()),xs)) -> Cons(S(x),addlist(xs',xs)) addlist(Cons(S(0()),xs'),Cons(x,xs)) -> Cons(S(x),addlist(xs',xs)) addlist(Nil(),ys) -> Nil() goal(xs,ys) -> addlist(xs,ys) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() - Signature: {addlist/2,goal/2,notEmpty/1} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {addlist,goal,notEmpty} 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"(8) 0 :: [] -(0)-> "A"(1) Cons :: ["A"(1) x "A"(1)] -(1)-> "A"(1) Cons :: ["A"(8) x "A"(8)] -(8)-> "A"(8) Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) False :: [] -(0)-> "A"(14) Nil :: [] -(0)-> "A"(1) Nil :: [] -(0)-> "A"(0) Nil :: [] -(0)-> "A"(6) S :: ["A"(8)] -(0)-> "A"(8) S :: ["A"(1)] -(0)-> "A"(1) S :: ["A"(0)] -(0)-> "A"(0) True :: [] -(0)-> "A"(14) addlist :: ["A"(1) x "A"(8)] -(4)-> "A"(0) goal :: ["A"(15) x "A"(14)] -(9)-> "A"(0) notEmpty :: ["A"(0)] -(5)-> "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)] -(0)-> "A"(1) "True_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))