MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            c() -> f(g(c()))
            f(g(X)) -> g(X)
        - Signature:
            {c/0,f/1} / {g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {c,f} and constructors {g}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          c#() -> c_1(f#(g(c())),c#())
          f#(g(X)) -> c_2()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            c#() -> c_1(f#(g(c())),c#())
            f#(g(X)) -> c_2()
        - Weak TRS:
            c() -> f(g(c()))
            f(g(X)) -> g(X)
        - Signature:
            {c/0,f/1,c#/0,f#/1} / {g/1,c_1/2,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {c#,f#} and constructors {g}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2}
        by application of
          Pre({2}) = {1}.
        Here rules are labelled as follows:
          1: c#() -> c_1(f#(g(c())),c#())
          2: f#(g(X)) -> c_2()
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            c#() -> c_1(f#(g(c())),c#())
        - Weak DPs:
            f#(g(X)) -> c_2()
        - Weak TRS:
            c() -> f(g(c()))
            f(g(X)) -> g(X)
        - Signature:
            {c/0,f/1,c#/0,f#/1} / {g/1,c_1/2,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {c#,f#} and constructors {g}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:c#() -> c_1(f#(g(c())),c#())
             -->_1 f#(g(X)) -> c_2():2
             -->_2 c#() -> c_1(f#(g(c())),c#()):1
          
          2:W:f#(g(X)) -> c_2()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: f#(g(X)) -> c_2()
* Step 4: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            c#() -> c_1(f#(g(c())),c#())
        - Weak TRS:
            c() -> f(g(c()))
            f(g(X)) -> g(X)
        - Signature:
            {c/0,f/1,c#/0,f#/1} / {g/1,c_1/2,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {c#,f#} and constructors {g}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:c#() -> c_1(f#(g(c())),c#())
             -->_2 c#() -> c_1(f#(g(c())),c#()):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          c#() -> c_1(c#())
* Step 5: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            c#() -> c_1(c#())
        - Weak TRS:
            c() -> f(g(c()))
            f(g(X)) -> g(X)
        - Signature:
            {c/0,f/1,c#/0,f#/1} / {g/1,c_1/1,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {c#,f#} and constructors {g}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          c#() -> c_1(c#())
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          c#() -> c_1(c#())
      - Signature:
          {c/0,f/1,c#/0,f#/1} / {g/1,c_1/1,c_2/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {c#,f#} and constructors {g}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE