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

** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a__f(X) -> f(X)
            a__f(f(a())) -> c(f(g(f(a()))))
            mark(a()) -> a()
            mark(c(X)) -> c(X)
            mark(f(X)) -> a__f(mark(X))
            mark(g(X)) -> g(mark(X))
        - Signature:
            {a__f/1,mark/1} / {a/0,c/1,f/1,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {a,c,f,g}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          a_0() -> 2
          a_1() -> 1
          a_1() -> 6
          a_1() -> 7
          a_2() -> 11
          a__f_0(2) -> 1
          a__f_1(7) -> 1
          a__f_1(7) -> 7
          c_0(2) -> 2
          c_1(2) -> 1
          c_1(2) -> 7
          c_1(3) -> 1
          c_2(8) -> 1
          c_2(8) -> 7
          f_0(2) -> 2
          f_1(2) -> 1
          f_1(4) -> 3
          f_1(6) -> 5
          f_2(7) -> 1
          f_2(7) -> 7
          f_2(9) -> 8
          f_2(11) -> 10
          g_0(2) -> 2
          g_1(5) -> 4
          g_1(7) -> 1
          g_1(7) -> 7
          g_2(10) -> 9
          mark_0(2) -> 1
          mark_1(2) -> 7
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a__f(X) -> f(X)
            a__f(f(a())) -> c(f(g(f(a()))))
            mark(a()) -> a()
            mark(c(X)) -> c(X)
            mark(f(X)) -> a__f(mark(X))
            mark(g(X)) -> g(mark(X))
        - Signature:
            {a__f/1,mark/1} / {a/0,c/1,f/1,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {a,c,f,g}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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