*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        a() -> n__a()
        activate(X) -> X
        activate(n__a()) -> a()
        activate(n__f(X)) -> f(X)
        activate(n__g(X)) -> g(activate(X))
        f(X) -> n__f(X)
        f(n__f(n__a())) -> f(n__g(n__f(n__a())))
        g(X) -> n__g(X)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1}
      Obligation:
        Full
        basic terms: {a,activate,f,g}/{n__a,n__f,n__g}
    Applied Processor:
      ToInnermost
    Proof:
      switch to innermost, as the system is overlay and right linear and does not contain weak rules
*** 1.1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        a() -> n__a()
        activate(X) -> X
        activate(n__a()) -> a()
        activate(n__f(X)) -> f(X)
        activate(n__g(X)) -> g(activate(X))
        f(X) -> n__f(X)
        f(n__f(n__a())) -> f(n__g(n__f(n__a())))
        g(X) -> n__g(X)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1}
      Obligation:
        Innermost
        basic terms: {a,activate,f,g}/{n__a,n__f,n__g}
    Applied Processor:
      Bounds {initialAutomaton = perSymbol, enrichment = match}
    Proof:
      The problem is match-bounded by 3.
      The enriched problem is compatible with follwoing automaton.
        a_0() -> 1
        a_1() -> 2
        a_1() -> 8
        activate_0(5) -> 2
        activate_0(6) -> 2
        activate_0(7) -> 2
        activate_1(5) -> 8
        activate_1(6) -> 8
        activate_1(7) -> 8
        activate_1(9) -> 8
        activate_2(9) -> 12
        f_0(5) -> 3
        f_0(6) -> 3
        f_0(7) -> 3
        f_1(5) -> 2
        f_1(5) -> 3
        f_1(5) -> 8
        f_1(6) -> 2
        f_1(6) -> 8
        f_1(7) -> 2
        f_1(7) -> 8
        f_2(1) -> 8
        f_2(1) -> 12
        g_0(5) -> 4
        g_0(6) -> 4
        g_0(7) -> 4
        g_1(8) -> 2
        g_1(8) -> 8
        g_2(12) -> 8
        n__a_0() -> 2
        n__a_0() -> 5
        n__a_0() -> 8
        n__a_1() -> 1
        n__a_2() -> 2
        n__a_2() -> 8
        n__f_0(5) -> 2
        n__f_0(5) -> 6
        n__f_0(5) -> 8
        n__f_0(6) -> 2
        n__f_0(6) -> 6
        n__f_0(6) -> 8
        n__f_0(7) -> 2
        n__f_0(7) -> 6
        n__f_0(7) -> 8
        n__f_1(1) -> 8
        n__f_1(1) -> 9
        n__f_1(1) -> 12
        n__f_1(5) -> 3
        n__f_1(6) -> 3
        n__f_1(7) -> 3
        n__f_2(5) -> 2
        n__f_2(5) -> 3
        n__f_2(5) -> 8
        n__f_2(6) -> 2
        n__f_2(6) -> 8
        n__f_2(7) -> 2
        n__f_2(7) -> 8
        n__f_3(1) -> 8
        n__f_3(1) -> 12
        n__g_0(5) -> 2
        n__g_0(5) -> 7
        n__g_0(5) -> 8
        n__g_0(6) -> 2
        n__g_0(6) -> 7
        n__g_0(6) -> 8
        n__g_0(7) -> 2
        n__g_0(7) -> 7
        n__g_0(7) -> 8
        n__g_1(5) -> 4
        n__g_1(6) -> 4
        n__g_1(7) -> 4
        n__g_1(9) -> 2
        n__g_1(9) -> 5
        n__g_1(9) -> 8
        n__g_2(8) -> 2
        n__g_2(8) -> 8
        n__g_3(12) -> 8
        5 -> 2
        5 -> 8
        6 -> 2
        6 -> 8
        7 -> 2
        7 -> 8
        9 -> 8
        9 -> 12
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        a() -> n__a()
        activate(X) -> X
        activate(n__a()) -> a()
        activate(n__f(X)) -> f(X)
        activate(n__g(X)) -> g(activate(X))
        f(X) -> n__f(X)
        f(n__f(n__a())) -> f(n__g(n__f(n__a())))
        g(X) -> n__g(X)
      Signature:
        {a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1}
      Obligation:
        Innermost
        basic terms: {a,activate,f,g}/{n__a,n__f,n__g}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).