* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(a(),a()) -> f(a(),b())
            f(a(),b()) -> f(s(a()),c())
            f(c(),c()) -> f(a(),a())
            f(s(X),c()) -> f(X,c())
        - Signature:
            {f/2} / {a/0,b/0,c/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {a,b,c,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(a(),a()) -> f(a(),b())
            f(a(),b()) -> f(s(a()),c())
            f(c(),c()) -> f(a(),a())
            f(s(X),c()) -> f(X,c())
        - Signature:
            {f/2} / {a/0,b/0,c/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {a,b,c,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          f(x,c()){x -> s(x)} =
            f(s(x),c()) ->^+ f(x,c())
              = C[f(x,c()) = f(x,c()){}]

** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(a(),a()) -> f(a(),b())
            f(a(),b()) -> f(s(a()),c())
            f(c(),c()) -> f(a(),a())
            f(s(X),c()) -> f(X,c())
        - Signature:
            {f/2} / {a/0,b/0,c/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {a,b,c,s}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 4.
        The enriched problem is compatible with follwoing automaton.
          a_0() -> 1
          a_1() -> 6
          a_2() -> 10
          a_3() -> 13
          b_0() -> 2
          b_1() -> 7
          b_2() -> 12
          c_0() -> 3
          c_1() -> 7
          c_2() -> 9
          c_3() -> 11
          c_4() -> 14
          f_0(1,1) -> 4
          f_0(1,2) -> 4
          f_0(1,3) -> 4
          f_0(1,5) -> 4
          f_0(2,1) -> 4
          f_0(2,2) -> 4
          f_0(2,3) -> 4
          f_0(2,5) -> 4
          f_0(3,1) -> 4
          f_0(3,2) -> 4
          f_0(3,3) -> 4
          f_0(3,5) -> 4
          f_0(5,1) -> 4
          f_0(5,2) -> 4
          f_0(5,3) -> 4
          f_0(5,5) -> 4
          f_1(1,7) -> 4
          f_1(2,7) -> 4
          f_1(3,7) -> 4
          f_1(5,7) -> 4
          f_1(6,6) -> 4
          f_1(6,7) -> 4
          f_2(6,9) -> 4
          f_2(8,9) -> 4
          f_2(10,12) -> 4
          f_3(10,11) -> 4
          f_4(13,14) -> 4
          s_0(1) -> 5
          s_0(2) -> 5
          s_0(3) -> 5
          s_0(5) -> 5
          s_1(6) -> 6
          s_2(10) -> 8
          s_3(13) -> 10
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(a(),a()) -> f(a(),b())
            f(a(),b()) -> f(s(a()),c())
            f(c(),c()) -> f(a(),a())
            f(s(X),c()) -> f(X,c())
        - Signature:
            {f/2} / {a/0,b/0,c/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {a,b,c,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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