*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        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()
      Weak DP Rules:
        
      Weak TRS Rules:
        
      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
        basic terms: {comp_f_g#1,main,walk#1}/{Cons,Nil,comp_f_g,walk_xs,walk_xs_3}
    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(2,1) -> 1
        Cons_1(2,2) -> 1
        Cons_1(2,2) -> 3
        Cons_1(2,3) -> 1
        Cons_1(2,4) -> 1
        Cons_2(2,1) -> 1
        Cons_2(2,3) -> 1
        Cons_2(2,3) -> 4
        Cons_2(2,4) -> 1
        Nil_0() -> 2
        Nil_1() -> 1
        Nil_1() -> 3
        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(2,2,1) -> 1
        comp_f_g#1_1(2,2,3) -> 1
        comp_f_g#1_2(2,2,1) -> 1
        comp_f_g#1_2(2,2,4) -> 1
        main_0(2) -> 1
        walk#1_0(2) -> 1
        walk#1_1(2) -> 2
        walk_xs_0() -> 2
        walk_xs_1() -> 1
        walk_xs_1() -> 2
        walk_xs_3_0(2) -> 2
        walk_xs_3_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(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
        basic terms: {comp_f_g#1,main,walk#1}/{Cons,Nil,comp_f_g,walk_xs,walk_xs_3}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).