MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            f(0()) -> 0()
            f(S(x)) -> x
            g(x) -> g(x)
        - Signature:
            {f/1,g/1} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,S}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          f#(0()) -> c_1()
          f#(S(x)) -> c_2()
          g#(x) -> c_3(g#(x))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(0()) -> c_1()
            f#(S(x)) -> c_2()
            g#(x) -> c_3(g#(x))
        - Weak TRS:
            f(0()) -> 0()
            f(S(x)) -> x
            g(x) -> g(x)
        - Signature:
            {f/1,g/1,f#/1,g#/1} / {0/0,S/1,c_1/0,c_2/0,c_3/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#} and constructors {0,S}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          f#(0()) -> c_1()
          f#(S(x)) -> c_2()
          g#(x) -> c_3(g#(x))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(0()) -> c_1()
            f#(S(x)) -> c_2()
            g#(x) -> c_3(g#(x))
        - Signature:
            {f/1,g/1,f#/1,g#/1} / {0/0,S/1,c_1/0,c_2/0,c_3/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#} and constructors {0,S}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2}
        by application of
          Pre({1,2}) = {}.
        Here rules are labelled as follows:
          1: f#(0()) -> c_1()
          2: f#(S(x)) -> c_2()
          3: g#(x) -> c_3(g#(x))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            g#(x) -> c_3(g#(x))
        - Weak DPs:
            f#(0()) -> c_1()
            f#(S(x)) -> c_2()
        - Signature:
            {f/1,g/1,f#/1,g#/1} / {0/0,S/1,c_1/0,c_2/0,c_3/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,g#} and constructors {0,S}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:g#(x) -> c_3(g#(x))
             -->_1 g#(x) -> c_3(g#(x)):1
          
          2:W:f#(0()) -> c_1()
             
          
          3:W:f#(S(x)) -> c_2()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: f#(S(x)) -> c_2()
          2: f#(0()) -> c_1()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          g#(x) -> c_3(g#(x))
      - Signature:
          {f/1,g/1,f#/1,g#/1} / {0/0,S/1,c_1/0,c_2/0,c_3/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {f#,g#} and constructors {0,S}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE