MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__h(X)) -> h(X)
            f(X) -> g(n__h(f(X)))
            h(X) -> n__h(X)
        - Signature:
            {activate/1,f/1,h/1} / {g/1,n__h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,f,h} and constructors {g,n__h}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          activate#(X) -> c_1()
          activate#(n__h(X)) -> c_2(h#(X))
          f#(X) -> c_3(f#(X))
          h#(X) -> c_4()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__h(X)) -> c_2(h#(X))
            f#(X) -> c_3(f#(X))
            h#(X) -> c_4()
        - Weak TRS:
            activate(X) -> X
            activate(n__h(X)) -> h(X)
            f(X) -> g(n__h(f(X)))
            h(X) -> n__h(X)
        - Signature:
            {activate/1,f/1,h/1,activate#/1,f#/1,h#/1} / {g/1,n__h/1,c_1/0,c_2/1,c_3/1,c_4/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,f#,h#} and constructors {g,n__h}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate#(X) -> c_1()
          activate#(n__h(X)) -> c_2(h#(X))
          f#(X) -> c_3(f#(X))
          h#(X) -> c_4()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__h(X)) -> c_2(h#(X))
            f#(X) -> c_3(f#(X))
            h#(X) -> c_4()
        - Signature:
            {activate/1,f/1,h/1,activate#/1,f#/1,h#/1} / {g/1,n__h/1,c_1/0,c_2/1,c_3/1,c_4/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,f#,h#} and constructors {g,n__h}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4}
        by application of
          Pre({1,4}) = {2}.
        Here rules are labelled as follows:
          1: activate#(X) -> c_1()
          2: activate#(n__h(X)) -> c_2(h#(X))
          3: f#(X) -> c_3(f#(X))
          4: h#(X) -> c_4()
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__h(X)) -> c_2(h#(X))
            f#(X) -> c_3(f#(X))
        - Weak DPs:
            activate#(X) -> c_1()
            h#(X) -> c_4()
        - Signature:
            {activate/1,f/1,h/1,activate#/1,f#/1,h#/1} / {g/1,n__h/1,c_1/0,c_2/1,c_3/1,c_4/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,f#,h#} and constructors {g,n__h}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {}.
        Here rules are labelled as follows:
          1: activate#(n__h(X)) -> c_2(h#(X))
          2: f#(X) -> c_3(f#(X))
          3: activate#(X) -> c_1()
          4: h#(X) -> c_4()
* Step 5: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(X) -> c_3(f#(X))
        - Weak DPs:
            activate#(X) -> c_1()
            activate#(n__h(X)) -> c_2(h#(X))
            h#(X) -> c_4()
        - Signature:
            {activate/1,f/1,h/1,activate#/1,f#/1,h#/1} / {g/1,n__h/1,c_1/0,c_2/1,c_3/1,c_4/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,f#,h#} and constructors {g,n__h}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:f#(X) -> c_3(f#(X))
             -->_1 f#(X) -> c_3(f#(X)):1
          
          2:W:activate#(X) -> c_1()
             
          
          3:W:activate#(n__h(X)) -> c_2(h#(X))
             -->_1 h#(X) -> c_4():4
          
          4:W:h#(X) -> c_4()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: activate#(n__h(X)) -> c_2(h#(X))
          4: h#(X) -> c_4()
          2: activate#(X) -> c_1()
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          f#(X) -> c_3(f#(X))
      - Signature:
          {activate/1,f/1,h/1,activate#/1,f#/1,h#/1} / {g/1,n__h/1,c_1/0,c_2/1,c_3/1,c_4/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,f#,h#} and constructors {g,n__h}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE