*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        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))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      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
        basic terms: {comp_f_g#1,main,walk#1}/{Cons,Leaf,Nil,Node,comp_f_g,cons_x}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 2.
      The enriched problem is compatible with follwoing automaton.
        Cons_0(2,2) -> 2
        Cons_1(2,2) -> 2
        Cons_1(2,2) -> 3
        Cons_1(2,2) -> 4
        Cons_1(2,3) -> 1
        Cons_1(2,3) -> 3
        Cons_1(2,3) -> 4
        Cons_1(2,3) -> 5
        Cons_1(2,4) -> 2
        Cons_1(2,5) -> 3
        Cons_1(2,5) -> 5
        Cons_2(2,2) -> 4
        Cons_2(2,3) -> 5
        Cons_2(2,4) -> 2
        Cons_2(2,4) -> 3
        Cons_2(2,4) -> 4
        Cons_2(2,5) -> 1
        Cons_2(2,5) -> 3
        Cons_2(2,5) -> 4
        Cons_2(2,5) -> 5
        Leaf_0(2) -> 2
        Nil_0() -> 2
        Nil_1() -> 3
        Node_0(2,2) -> 2
        comp_f_g_0(2,2) -> 2
        comp_f_g_1(2,2) -> 1
        comp_f_g_1(2,2) -> 2
        comp_f_g#1_0(2,2,2) -> 1
        comp_f_g#1_1(2,2,2) -> 2
        comp_f_g#1_1(2,2,2) -> 3
        comp_f_g#1_1(2,2,2) -> 4
        comp_f_g#1_1(2,2,3) -> 1
        comp_f_g#1_1(2,2,3) -> 3
        comp_f_g#1_1(2,2,3) -> 4
        comp_f_g#1_1(2,2,3) -> 5
        comp_f_g#1_1(2,2,4) -> 2
        comp_f_g#1_1(2,2,5) -> 3
        comp_f_g#1_2(2,2,2) -> 4
        comp_f_g#1_2(2,2,3) -> 5
        comp_f_g#1_2(2,2,4) -> 2
        comp_f_g#1_2(2,2,4) -> 3
        comp_f_g#1_2(2,2,4) -> 4
        comp_f_g#1_2(2,2,5) -> 1
        comp_f_g#1_2(2,2,5) -> 3
        comp_f_g#1_2(2,2,5) -> 4
        comp_f_g#1_2(2,2,5) -> 5
        cons_x_0(2) -> 2
        cons_x_1(2) -> 1
        cons_x_1(2) -> 2
        main_0(2) -> 1
        walk#1_0(2) -> 1
        walk#1_1(2) -> 2
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        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
        basic terms: {comp_f_g#1,main,walk#1}/{Cons,Leaf,Nil,Node,comp_f_g,cons_x}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).