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 {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- Cons :: [A(0) x A(0)] -(0)-> A(0) Cons :: [A(0) x A(0)] -(0)-> A(1) Leaf :: [A(0)] -(4)-> A(4) Nil :: [] -(0)-> A(1) Nil :: [] -(0)-> A(0) Node :: [A(4) x A(4)] -(4)-> A(4) comp_f_g :: [A(1) x A(1)] -(1)-> A(1) comp_f_g#1 :: [A(1) x A(1) x A(0)] -(0)-> A(0) cons_x :: [A(0)] -(1)-> A(1) main :: [A(4)] -(4)-> A(0) walk#1 :: [A(4)] -(1)-> A(1) Cost-free Signatures used: -------------------------- Cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) Leaf :: [A_cf(0)] -(0)-> A_cf(0) Node :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) comp_f_g :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0) comp_f_g#1 :: [A_cf(0) x A_cf(0) x A_cf(0)] -(0)-> A_cf(0) cons_x :: [A_cf(0)] -(0)-> A_cf(0) walk#1 :: [A_cf(0)] -(0)-> A_cf(0) Base Constructor Signatures used: --------------------------------- Cons_A :: [A(0) x A(0)] -(0)-> A(1) Leaf_A :: [A(0)] -(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) * Step 2: Open MAYBE - 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} Following problems could not be solved: - 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} WORST_CASE(?,O(n^1))