WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: comp_f_g#1(comp_f_g(x4,walk_xyz_3(x3)),walk_xyz_3(x2),x1) -> comp_f_g#1(x4,walk_xyz_3(x3),Cons(x2,x1)) comp_f_g#1(walk_xyz(),walk_xyz_3(x3),Cons(x1,x2)) -> Cons(x3,Cons(x1,x2)) main() -> comp_f_g#1(walk#1(Cons(S(S(0())),Cons(S(S(S(0()))),Nil()))),walk_xyz_3(S(0())),Nil()) walk#1(Cons(x4,x3)) -> comp_f_g(walk#1(x3),walk_xyz_3(x4)) walk#1(Nil()) -> walk_xyz() - Signature: {comp_f_g#1/3,main/0,walk#1/1} / {0/0,Cons/2,Nil/0,S/1,comp_f_g/2,walk_xyz/0,walk_xyz_3/1} - Obligation: innermost runtime complexity wrt. defined symbols {comp_f_g#1,main,walk#1} and constructors {0,Cons,Nil,S ,comp_f_g,walk_xyz,walk_xyz_3} + 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"(1)] -(1)-> "A"(1) Cons :: ["A"(0) x "A"(7)] -(7)-> "A"(7) Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) Nil :: [] -(0)-> "A"(7) Nil :: [] -(0)-> "A"(15) S :: ["A"(0)] -(0)-> "A"(15) S :: ["A"(0)] -(0)-> "A"(7) comp_f_g :: ["A"(2) x "A"(2)] -(2)-> "A"(2) comp_f_g#1 :: ["A"(2) x "A"(0) x "A"(1)] -(0)-> "A"(0) main :: [] -(16)-> "A"(0) walk#1 :: ["A"(7)] -(1)-> "A"(2) walk_xyz :: [] -(0)-> "A"(2) walk_xyz :: [] -(0)-> "A"(5) walk_xyz_3 :: ["A"(0)] -(2)-> "A"(2) walk_xyz_3 :: ["A"(0)] -(0)-> "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) "Nil_A" :: [] -(0)-> "A"(1) "S_A" :: ["A"(0)] -(0)-> "A"(1) "comp_f_g_A" :: ["A"(0) x "A"(0)] -(1)-> "A"(1) "walk_xyz_3_A" :: ["A"(0)] -(1)-> "A"(1) "walk_xyz_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))