WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: fold(a,xs) -> Cons(foldl(a,xs),Cons(foldr(a,xs),Nil())) foldl(a,Nil()) -> a foldl(x,Cons(S(0()),xs)) -> foldl(S(x),xs) foldl(S(0()),Cons(x,xs)) -> foldl(S(x),xs) foldr(a,Cons(x,xs)) -> op(x,foldr(a,xs)) foldr(a,Nil()) -> a notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() op(x,S(0())) -> S(x) op(S(0()),y) -> S(y) - Signature: {fold/2,foldl/2,foldr/2,notEmpty/1,op/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0} - Obligation: innermost runtime complexity wrt. defined symbols {fold,foldl,foldr,notEmpty,op} 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) Cons :: ["A"(0) x "A"(9)] -(9)-> "A"(9) Cons :: ["A"(0) x "A"(3)] -(3)-> "A"(3) Cons :: ["A"(0) x "A"(2)] -(2)-> "A"(2) Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) False :: [] -(0)-> "A"(14) Nil :: [] -(0)-> "A"(9) Nil :: [] -(0)-> "A"(3) Nil :: [] -(0)-> "A"(2) Nil :: [] -(0)-> "A"(13) S :: ["A"(0)] -(0)-> "A"(0) S :: ["A"(0)] -(4)-> "A"(4) S :: ["A"(0)] -(5)-> "A"(5) S :: ["A"(0)] -(7)-> "A"(7) True :: [] -(0)-> "A"(14) fold :: ["A"(15) x "A"(15)] -(16)-> "A"(0) foldl :: ["A"(4) x "A"(9)] -(1)-> "A"(0) foldr :: ["A"(1) x "A"(3)] -(9)-> "A"(0) notEmpty :: ["A"(2)] -(8)-> "A"(0) op :: ["A"(0) x "A"(0)] -(1)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1) "Cons_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1) "False_A" :: [] -(0)-> "A"(1) "Nil_A" :: [] -(0)-> "A"(1) "S_A" :: ["A"(0)] -(1)-> "A"(1) "True_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))