WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: apply#2(Lam1(x3,Lam3(x2)),x1) -> apply#2(x3,Cons(x2,x1)) apply#2(Lam2(),Cons(x1,x2)) -> Cons(x1,x2) main() -> apply#2(walk#1(Cons(S(0()),Cons(S(S(0())),Cons(S(S(S(0()))),Nil())))),Nil()) walk#1(Cons(x4,x3)) -> Lam1(walk#1(x3),Lam3(x4)) walk#1(Nil()) -> Lam2() - Signature: {apply#2/2,main/0,walk#1/1} / {0/0,Cons/2,Lam1/2,Lam2/0,Lam3/1,Nil/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {apply#2,main,walk#1} and constructors {0,Cons,Lam1,Lam2 ,Lam3,Nil,S} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- 0 :: [] -(0)-> "A"(15) Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) Cons :: ["A"(0) x "A"(2)] -(2)-> "A"(2) Lam1 :: ["A"(1) x "A"(1)] -(0)-> "A"(1) Lam2 :: [] -(0)-> "A"(1) Lam2 :: [] -(0)-> "A"(7) Lam3 :: ["A"(0)] -(1)-> "A"(1) Nil :: [] -(0)-> "A"(2) Nil :: [] -(0)-> "A"(15) Nil :: [] -(0)-> "A"(7) S :: ["A"(0)] -(0)-> "A"(11) S :: ["A"(0)] -(0)-> "A"(15) apply#2 :: ["A"(1) x "A"(0)] -(1)-> "A"(0) main :: [] -(16)-> "A"(0) walk#1 :: ["A"(2)] -(8)-> "A"(1) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1) "Cons_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1) "Lam1_A" :: ["A"(1) x "A"(1)] -(0)-> "A"(1) "Lam2_A" :: [] -(0)-> "A"(1) "Lam3_A" :: ["A"(0)] -(1)-> "A"(1) "Nil_A" :: [] -(0)-> "A"(1) "S_A" :: ["A"(0)] -(0)-> "A"(1) WORST_CASE(?,O(n^1))