MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__f(X1,X2)) -> f(X1,X2)
            f(X1,X2) -> n__f(X1,X2)
            f(g(X),Y) -> f(X,n__f(g(X),activate(Y)))
        - Signature:
            {activate/1,f/2} / {g/1,n__f/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,f} and constructors {g,n__f}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          activate#(X) -> c_1()
          activate#(n__f(X1,X2)) -> c_2(f#(X1,X2))
          f#(X1,X2) -> c_3()
          f#(g(X),Y) -> c_4(f#(X,n__f(g(X),activate(Y))),activate#(Y))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__f(X1,X2)) -> c_2(f#(X1,X2))
            f#(X1,X2) -> c_3()
            f#(g(X),Y) -> c_4(f#(X,n__f(g(X),activate(Y))),activate#(Y))
        - Weak TRS:
            activate(X) -> X
            activate(n__f(X1,X2)) -> f(X1,X2)
            f(X1,X2) -> n__f(X1,X2)
            f(g(X),Y) -> f(X,n__f(g(X),activate(Y)))
        - Signature:
            {activate/1,f/2,activate#/1,f#/2} / {g/1,n__f/2,c_1/0,c_2/1,c_3/0,c_4/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,f#} and constructors {g,n__f}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3}
        by application of
          Pre({1,3}) = {2,4}.
        Here rules are labelled as follows:
          1: activate#(X) -> c_1()
          2: activate#(n__f(X1,X2)) -> c_2(f#(X1,X2))
          3: f#(X1,X2) -> c_3()
          4: f#(g(X),Y) -> c_4(f#(X,n__f(g(X),activate(Y))),activate#(Y))
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__f(X1,X2)) -> c_2(f#(X1,X2))
            f#(g(X),Y) -> c_4(f#(X,n__f(g(X),activate(Y))),activate#(Y))
        - Weak DPs:
            activate#(X) -> c_1()
            f#(X1,X2) -> c_3()
        - Weak TRS:
            activate(X) -> X
            activate(n__f(X1,X2)) -> f(X1,X2)
            f(X1,X2) -> n__f(X1,X2)
            f(g(X),Y) -> f(X,n__f(g(X),activate(Y)))
        - Signature:
            {activate/1,f/2,activate#/1,f#/2} / {g/1,n__f/2,c_1/0,c_2/1,c_3/0,c_4/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,f#} and constructors {g,n__f}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:activate#(n__f(X1,X2)) -> c_2(f#(X1,X2))
             -->_1 f#(g(X),Y) -> c_4(f#(X,n__f(g(X),activate(Y))),activate#(Y)):2
             -->_1 f#(X1,X2) -> c_3():4
          
          2:S:f#(g(X),Y) -> c_4(f#(X,n__f(g(X),activate(Y))),activate#(Y))
             -->_1 f#(X1,X2) -> c_3():4
             -->_2 activate#(X) -> c_1():3
             -->_1 f#(g(X),Y) -> c_4(f#(X,n__f(g(X),activate(Y))),activate#(Y)):2
             -->_2 activate#(n__f(X1,X2)) -> c_2(f#(X1,X2)):1
          
          3:W:activate#(X) -> c_1()
             
          
          4:W:f#(X1,X2) -> c_3()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: activate#(X) -> c_1()
          4: f#(X1,X2) -> c_3()
* Step 4: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          activate#(n__f(X1,X2)) -> c_2(f#(X1,X2))
          f#(g(X),Y) -> c_4(f#(X,n__f(g(X),activate(Y))),activate#(Y))
      - Weak TRS:
          activate(X) -> X
          activate(n__f(X1,X2)) -> f(X1,X2)
          f(X1,X2) -> n__f(X1,X2)
          f(g(X),Y) -> f(X,n__f(g(X),activate(Y)))
      - Signature:
          {activate/1,f/2,activate#/1,f#/2} / {g/1,n__f/2,c_1/0,c_2/1,c_3/0,c_4/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,f#} and constructors {g,n__f}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE