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,x5),comp_f_g(x2,x3),x1) -> comp_f_g#1(x4,x5,comp_f_g#1(x2,x3,x1)) comp_f_g#1(comp_f_g(x7,x9),cons_x(x2),x4) -> comp_f_g#1(x7,x9,Cons(x2,x4)) comp_f_g#1(cons_x(x2),comp_f_g(x5,x7),x3) -> Cons(x2,comp_f_g#1(x5,x7,x3)) comp_f_g#1(cons_x(x5),cons_x(x2),x4) -> Cons(x5,Cons(x2,x4)) main(Leaf(x4)) -> Cons(x4,Nil()) main(Node(x9,x5)) -> comp_f_g#1(walk#1(x9),walk#1(x5),Nil()) walk#1(Leaf(x2)) -> cons_x(x2) walk#1(Node(x5,x3)) -> comp_f_g(walk#1(x5),walk#1(x3)) - Signature: {comp_f_g#1/3,main/1,walk#1/1} / {Cons/2,Leaf/1,Nil/0,Node/2,comp_f_g/2,cons_x/1} - Obligation: innermost runtime complexity wrt. defined symbols {comp_f_g#1,main,walk#1} and constructors {Cons,Leaf,Nil ,Node,comp_f_g,cons_x} + Applied Processor: Ara {araHeuristics = NoHeuristics, minDegree = 1, maxDegree = 2, araTimeout = 5, araRuleShifting = Nothing} + Details: Signatures used: ---------------- Cons :: ["A"(3) x "A"(3)] -(0)-> "A"(3) Cons :: ["A"(1) x "A"(1)] -(0)-> "A"(1) Leaf :: ["A"(15)] -(15)-> "A"(15) Nil :: [] -(0)-> "A"(15) Nil :: [] -(0)-> "A"(14) Node :: ["A"(15) x "A"(15)] -(15)-> "A"(15) comp_f_g :: ["A"(14) x "A"(14)] -(14)-> "A"(14) comp_f_g#1 :: ["A"(14) x "A"(14) x "A"(3)] -(2)-> "A"(3) cons_x :: ["A"(14)] -(14)-> "A"(14) main :: ["A"(15)] -(3)-> "A"(1) walk#1 :: ["A"(15)] -(0)-> "A"(14) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "Cons_A" :: ["A"(1) x "A"(1)] -(0)-> "A"(1) "Leaf_A" :: ["A"(1)] -(1)-> "A"(1) "Nil_A" :: [] -(0)-> "A"(1) "Node_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "comp_f_g_A" :: ["A"(0) x "A"(0)] -(1)-> "A"(1) "cons_x_A" :: ["A"(0)] -(1)-> "A"(1) WORST_CASE(?,O(n^1))