MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__c()) -> c()
            activate(n__g(X)) -> g(X)
            c() -> f(n__g(n__c()))
            c() -> n__c()
            f(n__g(X)) -> g(activate(X))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,c/0,f/1,g/1} / {n__c/0,n__g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,c,f,g} and constructors {n__c,n__g}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          activate#(X) -> c_1()
          activate#(n__c()) -> c_2(c#())
          activate#(n__g(X)) -> c_3(g#(X))
          c#() -> c_4(f#(n__g(n__c())))
          c#() -> c_5()
          f#(n__g(X)) -> c_6(g#(activate(X)),activate#(X))
          g#(X) -> c_7()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__c()) -> c_2(c#())
            activate#(n__g(X)) -> c_3(g#(X))
            c#() -> c_4(f#(n__g(n__c())))
            c#() -> c_5()
            f#(n__g(X)) -> c_6(g#(activate(X)),activate#(X))
            g#(X) -> c_7()
        - Weak TRS:
            activate(X) -> X
            activate(n__c()) -> c()
            activate(n__g(X)) -> g(X)
            c() -> f(n__g(n__c()))
            c() -> n__c()
            f(n__g(X)) -> g(activate(X))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,c/0,f/1,g/1,activate#/1,c#/0,f#/1,g#/1} / {n__c/0,n__g/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0,c_6/2
            ,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,f#,g#} and constructors {n__c,n__g}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,5,7}
        by application of
          Pre({1,5,7}) = {2,3,6}.
        Here rules are labelled as follows:
          1: activate#(X) -> c_1()
          2: activate#(n__c()) -> c_2(c#())
          3: activate#(n__g(X)) -> c_3(g#(X))
          4: c#() -> c_4(f#(n__g(n__c())))
          5: c#() -> c_5()
          6: f#(n__g(X)) -> c_6(g#(activate(X)),activate#(X))
          7: g#(X) -> c_7()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__c()) -> c_2(c#())
            activate#(n__g(X)) -> c_3(g#(X))
            c#() -> c_4(f#(n__g(n__c())))
            f#(n__g(X)) -> c_6(g#(activate(X)),activate#(X))
        - Weak DPs:
            activate#(X) -> c_1()
            c#() -> c_5()
            g#(X) -> c_7()
        - Weak TRS:
            activate(X) -> X
            activate(n__c()) -> c()
            activate(n__g(X)) -> g(X)
            c() -> f(n__g(n__c()))
            c() -> n__c()
            f(n__g(X)) -> g(activate(X))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,c/0,f/1,g/1,activate#/1,c#/0,f#/1,g#/1} / {n__c/0,n__g/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0,c_6/2
            ,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,f#,g#} and constructors {n__c,n__g}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2}
        by application of
          Pre({2}) = {4}.
        Here rules are labelled as follows:
          1: activate#(n__c()) -> c_2(c#())
          2: activate#(n__g(X)) -> c_3(g#(X))
          3: c#() -> c_4(f#(n__g(n__c())))
          4: f#(n__g(X)) -> c_6(g#(activate(X)),activate#(X))
          5: activate#(X) -> c_1()
          6: c#() -> c_5()
          7: g#(X) -> c_7()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__c()) -> c_2(c#())
            c#() -> c_4(f#(n__g(n__c())))
            f#(n__g(X)) -> c_6(g#(activate(X)),activate#(X))
        - Weak DPs:
            activate#(X) -> c_1()
            activate#(n__g(X)) -> c_3(g#(X))
            c#() -> c_5()
            g#(X) -> c_7()
        - Weak TRS:
            activate(X) -> X
            activate(n__c()) -> c()
            activate(n__g(X)) -> g(X)
            c() -> f(n__g(n__c()))
            c() -> n__c()
            f(n__g(X)) -> g(activate(X))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,c/0,f/1,g/1,activate#/1,c#/0,f#/1,g#/1} / {n__c/0,n__g/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0,c_6/2
            ,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,f#,g#} and constructors {n__c,n__g}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:activate#(n__c()) -> c_2(c#())
             -->_1 c#() -> c_4(f#(n__g(n__c()))):2
             -->_1 c#() -> c_5():6
          
          2:S:c#() -> c_4(f#(n__g(n__c())))
             -->_1 f#(n__g(X)) -> c_6(g#(activate(X)),activate#(X)):3
          
          3:S:f#(n__g(X)) -> c_6(g#(activate(X)),activate#(X))
             -->_2 activate#(n__g(X)) -> c_3(g#(X)):5
             -->_1 g#(X) -> c_7():7
             -->_2 activate#(X) -> c_1():4
             -->_2 activate#(n__c()) -> c_2(c#()):1
          
          4:W:activate#(X) -> c_1()
             
          
          5:W:activate#(n__g(X)) -> c_3(g#(X))
             -->_1 g#(X) -> c_7():7
          
          6:W:c#() -> c_5()
             
          
          7:W:g#(X) -> c_7()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          6: c#() -> c_5()
          4: activate#(X) -> c_1()
          5: activate#(n__g(X)) -> c_3(g#(X))
          7: g#(X) -> c_7()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__c()) -> c_2(c#())
            c#() -> c_4(f#(n__g(n__c())))
            f#(n__g(X)) -> c_6(g#(activate(X)),activate#(X))
        - Weak TRS:
            activate(X) -> X
            activate(n__c()) -> c()
            activate(n__g(X)) -> g(X)
            c() -> f(n__g(n__c()))
            c() -> n__c()
            f(n__g(X)) -> g(activate(X))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,c/0,f/1,g/1,activate#/1,c#/0,f#/1,g#/1} / {n__c/0,n__g/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0,c_6/2
            ,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,f#,g#} and constructors {n__c,n__g}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:activate#(n__c()) -> c_2(c#())
             -->_1 c#() -> c_4(f#(n__g(n__c()))):2
          
          2:S:c#() -> c_4(f#(n__g(n__c())))
             -->_1 f#(n__g(X)) -> c_6(g#(activate(X)),activate#(X)):3
          
          3:S:f#(n__g(X)) -> c_6(g#(activate(X)),activate#(X))
             -->_2 activate#(n__c()) -> c_2(c#()):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          f#(n__g(X)) -> c_6(activate#(X))
* Step 6: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__c()) -> c_2(c#())
            c#() -> c_4(f#(n__g(n__c())))
            f#(n__g(X)) -> c_6(activate#(X))
        - Weak TRS:
            activate(X) -> X
            activate(n__c()) -> c()
            activate(n__g(X)) -> g(X)
            c() -> f(n__g(n__c()))
            c() -> n__c()
            f(n__g(X)) -> g(activate(X))
            g(X) -> n__g(X)
        - Signature:
            {activate/1,c/0,f/1,g/1,activate#/1,c#/0,f#/1,g#/1} / {n__c/0,n__g/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0,c_6/1
            ,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,f#,g#} and constructors {n__c,n__g}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate#(n__c()) -> c_2(c#())
          c#() -> c_4(f#(n__g(n__c())))
          f#(n__g(X)) -> c_6(activate#(X))
* Step 7: WeightGap MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__c()) -> c_2(c#())
            c#() -> c_4(f#(n__g(n__c())))
            f#(n__g(X)) -> c_6(activate#(X))
        - Signature:
            {activate/1,c/0,f/1,g/1,activate#/1,c#/0,f#/1,g#/1} / {n__c/0,n__g/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0,c_6/1
            ,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,f#,g#} and constructors {n__c,n__g}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 0, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
          The following argument positions are considered usable:
            uargs(c_2) = {1},
            uargs(c_4) = {1},
            uargs(c_6) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
             p(activate) = [0]         
                    p(c) = [0]         
                    p(f) = [0]         
                    p(g) = [0]         
                 p(n__c) = [0]         
                 p(n__g) = [0]         
            p(activate#) = [14]        
                   p(c#) = [0]         
                   p(f#) = [15]        
                   p(g#) = [0]         
                  p(c_1) = [0]         
                  p(c_2) = [1] x1 + [0]
                  p(c_3) = [0]         
                  p(c_4) = [1] x1 + [0]
                  p(c_5) = [0]         
                  p(c_6) = [1] x1 + [0]
                  p(c_7) = [0]         
          
          Following rules are strictly oriented:
          activate#(n__c()) = [14]             
                            > [0]              
                            = c_2(c#())        
          
                f#(n__g(X)) = [15]             
                            > [14]             
                            = c_6(activate#(X))
          
          
          Following rules are (at-least) weakly oriented:
          c#() =  [0]                  
               >= [15]                 
               =  c_4(f#(n__g(n__c())))
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 8: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          c#() -> c_4(f#(n__g(n__c())))
      - Weak DPs:
          activate#(n__c()) -> c_2(c#())
          f#(n__g(X)) -> c_6(activate#(X))
      - Signature:
          {activate/1,c/0,f/1,g/1,activate#/1,c#/0,f#/1,g#/1} / {n__c/0,n__g/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0,c_6/1
          ,c_7/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,c#,f#,g#} and constructors {n__c,n__g}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE