* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            active(f(X)) -> f(active(X))
            active(f(f(a()))) -> mark(f(g(f(a()))))
            f(mark(X)) -> mark(f(X))
            f(ok(X)) -> ok(f(X))
            g(ok(X)) -> ok(g(X))
            proper(a()) -> ok(a())
            proper(f(X)) -> f(proper(X))
            proper(g(X)) -> g(proper(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {a,mark,ok}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            active(f(X)) -> f(active(X))
            active(f(f(a()))) -> mark(f(g(f(a()))))
            f(mark(X)) -> mark(f(X))
            f(ok(X)) -> ok(f(X))
            g(ok(X)) -> ok(g(X))
            proper(a()) -> ok(a())
            proper(f(X)) -> f(proper(X))
            proper(g(X)) -> g(proper(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {a,mark,ok}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          f(x){x -> mark(x)} =
            f(mark(x)) ->^+ mark(f(x))
              = C[f(x) = f(x){}]

** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            active(f(X)) -> f(active(X))
            active(f(f(a()))) -> mark(f(g(f(a()))))
            f(mark(X)) -> mark(f(X))
            f(ok(X)) -> ok(f(X))
            g(ok(X)) -> ok(g(X))
            proper(a()) -> ok(a())
            proper(f(X)) -> f(proper(X))
            proper(g(X)) -> g(proper(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {a,mark,ok}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          a_0() -> 1
          a_1() -> 11
          active_0(1) -> 2
          active_0(5) -> 2
          active_0(6) -> 2
          active_1(1) -> 12
          active_1(5) -> 12
          active_1(6) -> 12
          active_2(11) -> 13
          f_0(1) -> 3
          f_0(5) -> 3
          f_0(6) -> 3
          f_1(1) -> 9
          f_1(5) -> 9
          f_1(6) -> 9
          g_0(1) -> 4
          g_0(5) -> 4
          g_0(6) -> 4
          g_1(1) -> 10
          g_1(5) -> 10
          g_1(6) -> 10
          mark_0(1) -> 5
          mark_0(5) -> 5
          mark_0(6) -> 5
          mark_1(9) -> 3
          mark_1(9) -> 9
          ok_0(1) -> 6
          ok_0(5) -> 6
          ok_0(6) -> 6
          ok_1(9) -> 3
          ok_1(9) -> 9
          ok_1(10) -> 4
          ok_1(10) -> 10
          ok_1(11) -> 7
          ok_1(11) -> 12
          proper_0(1) -> 7
          proper_0(5) -> 7
          proper_0(6) -> 7
          proper_1(1) -> 12
          proper_1(5) -> 12
          proper_1(6) -> 12
          top_0(1) -> 8
          top_0(5) -> 8
          top_0(6) -> 8
          top_1(12) -> 8
          top_2(13) -> 8
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            active(f(X)) -> f(active(X))
            active(f(f(a()))) -> mark(f(g(f(a()))))
            f(mark(X)) -> mark(f(X))
            f(ok(X)) -> ok(f(X))
            g(ok(X)) -> ok(g(X))
            proper(a()) -> ok(a())
            proper(f(X)) -> f(proper(X))
            proper(g(X)) -> g(proper(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,f/1,g/1,proper/1,top/1} / {a/0,mark/1,ok/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,f,g,proper,top} and constructors {a,mark,ok}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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