* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__d(X)) -> d(X)
            activate(n__f(X)) -> f(activate(X))
            activate(n__g(X)) -> g(X)
            c(X) -> d(activate(X))
            d(X) -> n__d(X)
            f(X) -> n__f(X)
            f(f(X)) -> c(n__f(n__g(n__f(X))))
            g(X) -> n__g(X)
            h(X) -> c(n__d(X))
        - Signature:
            {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,c,d,f,g,h} and constructors {n__d,n__f,n__g}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__d(X)) -> d(X)
            activate(n__f(X)) -> f(activate(X))
            activate(n__g(X)) -> g(X)
            c(X) -> d(activate(X))
            d(X) -> n__d(X)
            f(X) -> n__f(X)
            f(f(X)) -> c(n__f(n__g(n__f(X))))
            g(X) -> n__g(X)
            h(X) -> c(n__d(X))
        - Signature:
            {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,c,d,f,g,h} and constructors {n__d,n__f,n__g}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__f(x)} =
            activate(n__f(x)) ->^+ f(activate(x))
              = C[activate(x) = activate(x){}]

** Step 1.b:1: InnermostRuleRemoval WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__d(X)) -> d(X)
            activate(n__f(X)) -> f(activate(X))
            activate(n__g(X)) -> g(X)
            c(X) -> d(activate(X))
            d(X) -> n__d(X)
            f(X) -> n__f(X)
            f(f(X)) -> c(n__f(n__g(n__f(X))))
            g(X) -> n__g(X)
            h(X) -> c(n__d(X))
        - Signature:
            {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,c,d,f,g,h} and constructors {n__d,n__f,n__g}
    + Applied Processor:
        InnermostRuleRemoval
    + Details:
        Arguments of following rules are not normal-forms.
          f(f(X)) -> c(n__f(n__g(n__f(X))))
        All above mentioned rules can be savely removed.
** Step 1.b:2: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__d(X)) -> d(X)
            activate(n__f(X)) -> f(activate(X))
            activate(n__g(X)) -> g(X)
            c(X) -> d(activate(X))
            d(X) -> n__d(X)
            f(X) -> n__f(X)
            g(X) -> n__g(X)
            h(X) -> c(n__d(X))
        - Signature:
            {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,c,d,f,g,h} and constructors {n__d,n__f,n__g}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 4.
        The enriched problem is compatible with follwoing automaton.
          activate_0(2) -> 1
          activate_0(2) -> 4
          activate_1(2) -> 3
          activate_1(2) -> 6
          activate_2(1) -> 4
          activate_2(2) -> 5
          activate_3(3) -> 6
          c_0(2) -> 1
          c_0(2) -> 4
          c_1(1) -> 1
          c_1(1) -> 4
          d_0(2) -> 1
          d_0(2) -> 4
          d_1(2) -> 1
          d_1(2) -> 3
          d_1(2) -> 4
          d_1(2) -> 5
          d_1(2) -> 6
          d_1(3) -> 1
          d_1(3) -> 4
          d_2(2) -> 4
          d_2(4) -> 1
          d_2(4) -> 4
          d_3(2) -> 4
          d_3(2) -> 6
          d_3(3) -> 4
          d_3(4) -> 4
          f_0(2) -> 1
          f_0(2) -> 4
          f_1(3) -> 1
          f_1(3) -> 3
          f_1(3) -> 4
          f_1(3) -> 6
          f_1(6) -> 5
          f_2(5) -> 4
          f_3(6) -> 4
          f_3(6) -> 6
          g_0(2) -> 1
          g_0(2) -> 4
          g_1(2) -> 1
          g_1(2) -> 3
          g_1(2) -> 4
          g_1(2) -> 5
          g_1(2) -> 6
          g_2(2) -> 4
          g_3(2) -> 4
          g_3(2) -> 6
          h_0(2) -> 1
          h_0(2) -> 4
          n__d_0(2) -> 1
          n__d_0(2) -> 2
          n__d_0(2) -> 3
          n__d_0(2) -> 4
          n__d_0(2) -> 5
          n__d_0(2) -> 6
          n__d_1(2) -> 1
          n__d_1(2) -> 4
          n__d_2(2) -> 1
          n__d_2(2) -> 3
          n__d_2(2) -> 4
          n__d_2(2) -> 5
          n__d_2(2) -> 6
          n__d_2(3) -> 1
          n__d_2(3) -> 4
          n__d_3(2) -> 4
          n__d_3(4) -> 1
          n__d_3(4) -> 4
          n__d_4(2) -> 4
          n__d_4(2) -> 6
          n__d_4(3) -> 4
          n__d_4(4) -> 4
          n__f_0(2) -> 1
          n__f_0(2) -> 2
          n__f_0(2) -> 3
          n__f_0(2) -> 4
          n__f_0(2) -> 5
          n__f_0(2) -> 6
          n__f_1(2) -> 1
          n__f_1(2) -> 4
          n__f_2(3) -> 1
          n__f_2(3) -> 3
          n__f_2(3) -> 4
          n__f_2(3) -> 6
          n__f_2(6) -> 5
          n__f_3(5) -> 4
          n__f_4(6) -> 4
          n__f_4(6) -> 6
          n__g_0(2) -> 1
          n__g_0(2) -> 2
          n__g_0(2) -> 3
          n__g_0(2) -> 4
          n__g_0(2) -> 5
          n__g_0(2) -> 6
          n__g_1(2) -> 1
          n__g_1(2) -> 4
          n__g_2(2) -> 1
          n__g_2(2) -> 3
          n__g_2(2) -> 4
          n__g_2(2) -> 5
          n__g_2(2) -> 6
          n__g_3(2) -> 4
          n__g_4(2) -> 4
          n__g_4(2) -> 6
          1 -> 4
          2 -> 1
          2 -> 3
          2 -> 4
          2 -> 5
          2 -> 6
          3 -> 6
** Step 1.b:3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            activate(X) -> X
            activate(n__d(X)) -> d(X)
            activate(n__f(X)) -> f(activate(X))
            activate(n__g(X)) -> g(X)
            c(X) -> d(activate(X))
            d(X) -> n__d(X)
            f(X) -> n__f(X)
            g(X) -> n__g(X)
            h(X) -> c(n__d(X))
        - Signature:
            {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,c,d,f,g,h} and constructors {n__d,n__f,n__g}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^1))