WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: comp_f_g#1(comp_f_g(x7,x9),walk_xs_3(x8),x12) -> comp_f_g#1(x7,x9,Cons(x8,x12)) comp_f_g#1(walk_xs(),walk_xs_3(x8),x12) -> Cons(x8,x12) main(Cons(x4,x5)) -> comp_f_g#1(walk#1(x5),walk_xs_3(x4),Nil()) main(Nil()) -> Nil() walk#1(Cons(x4,x3)) -> comp_f_g(walk#1(x3),walk_xs_3(x4)) walk#1(Nil()) -> walk_xs() - Signature: {comp_f_g#1/3,main/1,walk#1/1} / {Cons/2,Nil/0,comp_f_g/2,walk_xs/0,walk_xs_3/1} - Obligation: innermost runtime complexity wrt. defined symbols {comp_f_g#1,main,walk#1} and constructors {Cons,Nil ,comp_f_g,walk_xs,walk_xs_3} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- Cons :: ["A"(0) x "A"(12)] -(12)-> "A"(12) Cons :: ["A"(0) x "A"(8)] -(8)-> "A"(8) Cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0) Nil :: [] -(0)-> "A"(12) Nil :: [] -(0)-> "A"(8) Nil :: [] -(0)-> "A"(10) Nil :: [] -(0)-> "A"(0) comp_f_g :: ["A"(3) x "A"(0)] -(3)-> "A"(3) comp_f_g#1 :: ["A"(3) x "A"(0) x "A"(0)] -(3)-> "A"(0) main :: ["A"(12)] -(15)-> "A"(0) walk#1 :: ["A"(8)] -(1)-> "A"(3) walk_xs :: [] -(0)-> "A"(3) walk_xs :: [] -(0)-> "A"(11) walk_xs_3 :: ["A"(0)] -(0)-> "A"(0) walk_xs_3 :: ["A"(0)] -(14)-> "A"(14) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "Cons_A" :: ["A"(0) x "A"(1)] -(1)-> "A"(1) "Nil_A" :: [] -(0)-> "A"(1) "comp_f_g_A" :: ["A"(0) x "A"(0)] -(1)-> "A"(1) "walk_xs_3_A" :: ["A"(0)] -(1)-> "A"(1) "walk_xs_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))