MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            f(g(X)) -> g(f(f(X)))
            f(h(X)) -> h(g(X))
        - Signature:
            {f/1} / {g/1,h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {g,h}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          f#(g(X)) -> c_1(f#(f(X)),f#(X))
          f#(h(X)) -> c_2()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(g(X)) -> c_1(f#(f(X)),f#(X))
            f#(h(X)) -> c_2()
        - Weak TRS:
            f(g(X)) -> g(f(f(X)))
            f(h(X)) -> h(g(X))
        - Signature:
            {f/1,f#/1} / {g/1,h/1,c_1/2,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#} and constructors {g,h}
    + 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: f#(g(X)) -> c_1(f#(f(X)),f#(X))
          2: f#(h(X)) -> c_2()
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(g(X)) -> c_1(f#(f(X)),f#(X))
        - Weak DPs:
            f#(h(X)) -> c_2()
        - Weak TRS:
            f(g(X)) -> g(f(f(X)))
            f(h(X)) -> h(g(X))
        - Signature:
            {f/1,f#/1} / {g/1,h/1,c_1/2,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#} and constructors {g,h}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:f#(g(X)) -> c_1(f#(f(X)),f#(X))
             -->_2 f#(h(X)) -> c_2():2
             -->_1 f#(h(X)) -> c_2():2
             -->_2 f#(g(X)) -> c_1(f#(f(X)),f#(X)):1
             -->_1 f#(g(X)) -> c_1(f#(f(X)),f#(X)):1
          
          2:W:f#(h(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#(h(X)) -> c_2()
* Step 4: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          f#(g(X)) -> c_1(f#(f(X)),f#(X))
      - Weak TRS:
          f(g(X)) -> g(f(f(X)))
          f(h(X)) -> h(g(X))
      - Signature:
          {f/1,f#/1} / {g/1,h/1,c_1/2,c_2/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {f#} and constructors {g,h}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE