MAYBE
* Step 1: InnermostRuleRemoval MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__g(X)) -> g(activate(X))
            b() -> c()
            f(X,n__g(X),Y) -> f(activate(Y),activate(Y),activate(Y))
            g(X) -> n__g(X)
            g(b()) -> c()
        - Signature:
            {activate/1,b/0,f/3,g/1} / {c/0,n__g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,b,f,g} and constructors {c,n__g}
    + Applied Processor:
        InnermostRuleRemoval
    + Details:
        Arguments of following rules are not normal-forms.
          g(b()) -> c()
        All above mentioned rules can be savely removed.
* Step 2: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__g(X)) -> g(activate(X))
            b() -> c()
            f(X,n__g(X),Y) -> f(activate(Y),activate(Y),activate(Y))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,b/0,f/3,g/1} / {c/0,n__g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,b,f,g} and constructors {c,n__g}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          activate#(X) -> c_1()
          activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X))
          b#() -> c_3()
          f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
          g#(X) -> c_5()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X))
            b#() -> c_3()
            f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
            g#(X) -> c_5()
        - Weak TRS:
            activate(X) -> X
            activate(n__g(X)) -> g(activate(X))
            b() -> c()
            f(X,n__g(X),Y) -> f(activate(Y),activate(Y),activate(Y))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,b/0,f/3,g/1,activate#/1,b#/0,f#/3,g#/1} / {c/0,n__g/1,c_1/0,c_2/2,c_3/0,c_4/4,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,b#,f#,g#} and constructors {c,n__g}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate(X) -> X
          activate(n__g(X)) -> g(activate(X))
          g(X) -> n__g(X)
          activate#(X) -> c_1()
          activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X))
          b#() -> c_3()
          f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
          g#(X) -> c_5()
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X))
            b#() -> c_3()
            f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
            g#(X) -> c_5()
        - Weak TRS:
            activate(X) -> X
            activate(n__g(X)) -> g(activate(X))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,b/0,f/3,g/1,activate#/1,b#/0,f#/3,g#/1} / {c/0,n__g/1,c_1/0,c_2/2,c_3/0,c_4/4,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,b#,f#,g#} and constructors {c,n__g}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,5}
        by application of
          Pre({1,3,5}) = {2,4}.
        Here rules are labelled as follows:
          1: activate#(X) -> c_1()
          2: activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X))
          3: b#() -> c_3()
          4: f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
          5: g#(X) -> c_5()
* Step 5: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X))
            f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
        - Weak DPs:
            activate#(X) -> c_1()
            b#() -> c_3()
            g#(X) -> c_5()
        - Weak TRS:
            activate(X) -> X
            activate(n__g(X)) -> g(activate(X))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,b/0,f/3,g/1,activate#/1,b#/0,f#/3,g#/1} / {c/0,n__g/1,c_1/0,c_2/2,c_3/0,c_4/4,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,b#,f#,g#} and constructors {c,n__g}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X))
             -->_1 g#(X) -> c_5():5
             -->_2 activate#(X) -> c_1():3
             -->_2 activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X)):1
          
          2:S:f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
             -->_4 activate#(X) -> c_1():3
             -->_3 activate#(X) -> c_1():3
             -->_2 activate#(X) -> c_1():3
             -->_1 f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y))
                                         ,activate#(Y)
                                         ,activate#(Y)
                                         ,activate#(Y)):2
             -->_4 activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X)):1
             -->_3 activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X)):1
             -->_2 activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X)):1
          
          3:W:activate#(X) -> c_1()
             
          
          4:W:b#() -> c_3()
             
          
          5:W:g#(X) -> c_5()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          4: b#() -> c_3()
          3: activate#(X) -> c_1()
          5: g#(X) -> c_5()
* Step 6: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X))
            f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
        - Weak TRS:
            activate(X) -> X
            activate(n__g(X)) -> g(activate(X))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,b/0,f/3,g/1,activate#/1,b#/0,f#/3,g#/1} / {c/0,n__g/1,c_1/0,c_2/2,c_3/0,c_4/4,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,b#,f#,g#} and constructors {c,n__g}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X))
             -->_2 activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X)):1
          
          2:S:f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
             -->_1 f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y))
                                         ,activate#(Y)
                                         ,activate#(Y)
                                         ,activate#(Y)):2
             -->_4 activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X)):1
             -->_3 activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X)):1
             -->_2 activate#(n__g(X)) -> c_2(g#(activate(X)),activate#(X)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          activate#(n__g(X)) -> c_2(activate#(X))
* Step 7: Decompose MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__g(X)) -> c_2(activate#(X))
            f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
        - Weak TRS:
            activate(X) -> X
            activate(n__g(X)) -> g(activate(X))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,b/0,f/3,g/1,activate#/1,b#/0,f#/3,g#/1} / {c/0,n__g/1,c_1/0,c_2/1,c_3/0,c_4/4,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,b#,f#,g#} and constructors {c,n__g}
    + Applied Processor:
        Decompose {onSelection = all cycle independent sub-graph, withBound = RelativeAdd}
    + Details:
        We analyse the complexity of following sub-problems (R) and (S).
        Problem (S) is obtained from the input problem by shifting strict rules from (R) into the weak component.
        
        Problem (R)
          - Strict DPs:
              activate#(n__g(X)) -> c_2(activate#(X))
          - Weak DPs:
              f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
          - Weak TRS:
              activate(X) -> X
              activate(n__g(X)) -> g(activate(X))
              g(X) -> n__g(X)
          - Signature:
              {activate/1,b/0,f/3,g/1,activate#/1,b#/0,f#/3,g#/1} / {c/0,n__g/1,c_1/0,c_2/1,c_3/0,c_4/4,c_5/0}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {activate#,b#,f#,g#} and constructors {c,n__g}
        
        Problem (S)
          - Strict DPs:
              f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
          - Weak DPs:
              activate#(n__g(X)) -> c_2(activate#(X))
          - Weak TRS:
              activate(X) -> X
              activate(n__g(X)) -> g(activate(X))
              g(X) -> n__g(X)
          - Signature:
              {activate/1,b/0,f/3,g/1,activate#/1,b#/0,f#/3,g#/1} / {c/0,n__g/1,c_1/0,c_2/1,c_3/0,c_4/4,c_5/0}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {activate#,b#,f#,g#} and constructors {c,n__g}
** Step 7.a:1: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          activate#(n__g(X)) -> c_2(activate#(X))
      - Weak DPs:
          f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
      - Weak TRS:
          activate(X) -> X
          activate(n__g(X)) -> g(activate(X))
          g(X) -> n__g(X)
      - Signature:
          {activate/1,b/0,f/3,g/1,activate#/1,b#/0,f#/3,g#/1} / {c/0,n__g/1,c_1/0,c_2/1,c_3/0,c_4/4,c_5/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,b#,f#,g#} and constructors {c,n__g}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
** Step 7.b:1: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
        - Weak DPs:
            activate#(n__g(X)) -> c_2(activate#(X))
        - Weak TRS:
            activate(X) -> X
            activate(n__g(X)) -> g(activate(X))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,b/0,f/3,g/1,activate#/1,b#/0,f#/3,g#/1} / {c/0,n__g/1,c_1/0,c_2/1,c_3/0,c_4/4,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,b#,f#,g#} and constructors {c,n__g}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
             -->_4 activate#(n__g(X)) -> c_2(activate#(X)):2
             -->_3 activate#(n__g(X)) -> c_2(activate#(X)):2
             -->_2 activate#(n__g(X)) -> c_2(activate#(X)):2
             -->_1 f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y))
                                         ,activate#(Y)
                                         ,activate#(Y)
                                         ,activate#(Y)):1
          
          2:W:activate#(n__g(X)) -> c_2(activate#(X))
             -->_1 activate#(n__g(X)) -> c_2(activate#(X)):2
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: activate#(n__g(X)) -> c_2(activate#(X))
** Step 7.b:2: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
        - Weak TRS:
            activate(X) -> X
            activate(n__g(X)) -> g(activate(X))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,b/0,f/3,g/1,activate#/1,b#/0,f#/3,g#/1} / {c/0,n__g/1,c_1/0,c_2/1,c_3/0,c_4/4,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,b#,f#,g#} and constructors {c,n__g}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)),activate#(Y),activate#(Y),activate#(Y))
             -->_1 f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y))
                                         ,activate#(Y)
                                         ,activate#(Y)
                                         ,activate#(Y)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)))
** Step 7.b:3: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          f#(X,n__g(X),Y) -> c_4(f#(activate(Y),activate(Y),activate(Y)))
      - Weak TRS:
          activate(X) -> X
          activate(n__g(X)) -> g(activate(X))
          g(X) -> n__g(X)
      - Signature:
          {activate/1,b/0,f/3,g/1,activate#/1,b#/0,f#/3,g#/1} / {c/0,n__g/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,b#,f#,g#} and constructors {c,n__g}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE