MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__c()) -> c()
            activate(n__d()) -> d()
            c() -> d()
            c() -> n__c()
            d() -> n__d()
            g(X) -> h(activate(X))
            h(n__d()) -> g(n__c())
        - Signature:
            {activate/1,c/0,d/0,g/1,h/1} / {n__c/0,n__d/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,c,d,g,h} and constructors {n__c,n__d}
    + 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__d()) -> c_3(d#())
          c#() -> c_4(d#())
          c#() -> c_5()
          d#() -> c_6()
          g#(X) -> c_7(h#(activate(X)),activate#(X))
          h#(n__d()) -> c_8(g#(n__c()))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__c()) -> c_2(c#())
            activate#(n__d()) -> c_3(d#())
            c#() -> c_4(d#())
            c#() -> c_5()
            d#() -> c_6()
            g#(X) -> c_7(h#(activate(X)),activate#(X))
            h#(n__d()) -> c_8(g#(n__c()))
        - Weak TRS:
            activate(X) -> X
            activate(n__c()) -> c()
            activate(n__d()) -> d()
            c() -> d()
            c() -> n__c()
            d() -> n__d()
            g(X) -> h(activate(X))
            h(n__d()) -> g(n__c())
        - Signature:
            {activate/1,c/0,d/0,g/1,h/1,activate#/1,c#/0,d#/0,g#/1,h#/1} / {n__c/0,n__d/0,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
            ,c_6/0,c_7/2,c_8/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,d#,g#,h#} and constructors {n__c,n__d}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate(X) -> X
          activate(n__c()) -> c()
          activate(n__d()) -> d()
          c() -> d()
          c() -> n__c()
          d() -> n__d()
          activate#(X) -> c_1()
          activate#(n__c()) -> c_2(c#())
          activate#(n__d()) -> c_3(d#())
          c#() -> c_4(d#())
          c#() -> c_5()
          d#() -> c_6()
          g#(X) -> c_7(h#(activate(X)),activate#(X))
          h#(n__d()) -> c_8(g#(n__c()))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__c()) -> c_2(c#())
            activate#(n__d()) -> c_3(d#())
            c#() -> c_4(d#())
            c#() -> c_5()
            d#() -> c_6()
            g#(X) -> c_7(h#(activate(X)),activate#(X))
            h#(n__d()) -> c_8(g#(n__c()))
        - Weak TRS:
            activate(X) -> X
            activate(n__c()) -> c()
            activate(n__d()) -> d()
            c() -> d()
            c() -> n__c()
            d() -> n__d()
        - Signature:
            {activate/1,c/0,d/0,g/1,h/1,activate#/1,c#/0,d#/0,g#/1,h#/1} / {n__c/0,n__d/0,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
            ,c_6/0,c_7/2,c_8/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,d#,g#,h#} and constructors {n__c,n__d}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,5,6}
        by application of
          Pre({1,5,6}) = {2,3,4,7}.
        Here rules are labelled as follows:
          1: activate#(X) -> c_1()
          2: activate#(n__c()) -> c_2(c#())
          3: activate#(n__d()) -> c_3(d#())
          4: c#() -> c_4(d#())
          5: c#() -> c_5()
          6: d#() -> c_6()
          7: g#(X) -> c_7(h#(activate(X)),activate#(X))
          8: h#(n__d()) -> c_8(g#(n__c()))
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__c()) -> c_2(c#())
            activate#(n__d()) -> c_3(d#())
            c#() -> c_4(d#())
            g#(X) -> c_7(h#(activate(X)),activate#(X))
            h#(n__d()) -> c_8(g#(n__c()))
        - Weak DPs:
            activate#(X) -> c_1()
            c#() -> c_5()
            d#() -> c_6()
        - Weak TRS:
            activate(X) -> X
            activate(n__c()) -> c()
            activate(n__d()) -> d()
            c() -> d()
            c() -> n__c()
            d() -> n__d()
        - Signature:
            {activate/1,c/0,d/0,g/1,h/1,activate#/1,c#/0,d#/0,g#/1,h#/1} / {n__c/0,n__d/0,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
            ,c_6/0,c_7/2,c_8/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,d#,g#,h#} and constructors {n__c,n__d}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,3}
        by application of
          Pre({2,3}) = {1,4}.
        Here rules are labelled as follows:
          1: activate#(n__c()) -> c_2(c#())
          2: activate#(n__d()) -> c_3(d#())
          3: c#() -> c_4(d#())
          4: g#(X) -> c_7(h#(activate(X)),activate#(X))
          5: h#(n__d()) -> c_8(g#(n__c()))
          6: activate#(X) -> c_1()
          7: c#() -> c_5()
          8: d#() -> c_6()
* Step 5: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__c()) -> c_2(c#())
            g#(X) -> c_7(h#(activate(X)),activate#(X))
            h#(n__d()) -> c_8(g#(n__c()))
        - Weak DPs:
            activate#(X) -> c_1()
            activate#(n__d()) -> c_3(d#())
            c#() -> c_4(d#())
            c#() -> c_5()
            d#() -> c_6()
        - Weak TRS:
            activate(X) -> X
            activate(n__c()) -> c()
            activate(n__d()) -> d()
            c() -> d()
            c() -> n__c()
            d() -> n__d()
        - Signature:
            {activate/1,c/0,d/0,g/1,h/1,activate#/1,c#/0,d#/0,g#/1,h#/1} / {n__c/0,n__d/0,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
            ,c_6/0,c_7/2,c_8/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,d#,g#,h#} and constructors {n__c,n__d}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {2}.
        Here rules are labelled as follows:
          1: activate#(n__c()) -> c_2(c#())
          2: g#(X) -> c_7(h#(activate(X)),activate#(X))
          3: h#(n__d()) -> c_8(g#(n__c()))
          4: activate#(X) -> c_1()
          5: activate#(n__d()) -> c_3(d#())
          6: c#() -> c_4(d#())
          7: c#() -> c_5()
          8: d#() -> c_6()
* Step 6: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            g#(X) -> c_7(h#(activate(X)),activate#(X))
            h#(n__d()) -> c_8(g#(n__c()))
        - Weak DPs:
            activate#(X) -> c_1()
            activate#(n__c()) -> c_2(c#())
            activate#(n__d()) -> c_3(d#())
            c#() -> c_4(d#())
            c#() -> c_5()
            d#() -> c_6()
        - Weak TRS:
            activate(X) -> X
            activate(n__c()) -> c()
            activate(n__d()) -> d()
            c() -> d()
            c() -> n__c()
            d() -> n__d()
        - Signature:
            {activate/1,c/0,d/0,g/1,h/1,activate#/1,c#/0,d#/0,g#/1,h#/1} / {n__c/0,n__d/0,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
            ,c_6/0,c_7/2,c_8/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,d#,g#,h#} and constructors {n__c,n__d}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:g#(X) -> c_7(h#(activate(X)),activate#(X))
             -->_2 activate#(n__d()) -> c_3(d#()):5
             -->_2 activate#(n__c()) -> c_2(c#()):4
             -->_1 h#(n__d()) -> c_8(g#(n__c())):2
             -->_2 activate#(X) -> c_1():3
          
          2:S:h#(n__d()) -> c_8(g#(n__c()))
             -->_1 g#(X) -> c_7(h#(activate(X)),activate#(X)):1
          
          3:W:activate#(X) -> c_1()
             
          
          4:W:activate#(n__c()) -> c_2(c#())
             -->_1 c#() -> c_4(d#()):6
             -->_1 c#() -> c_5():7
          
          5:W:activate#(n__d()) -> c_3(d#())
             -->_1 d#() -> c_6():8
          
          6:W:c#() -> c_4(d#())
             -->_1 d#() -> c_6():8
          
          7:W:c#() -> c_5()
             
          
          8:W:d#() -> c_6()
             
          
        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: activate#(n__c()) -> c_2(c#())
          7: c#() -> c_5()
          6: c#() -> c_4(d#())
          5: activate#(n__d()) -> c_3(d#())
          8: d#() -> c_6()
* Step 7: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            g#(X) -> c_7(h#(activate(X)),activate#(X))
            h#(n__d()) -> c_8(g#(n__c()))
        - Weak TRS:
            activate(X) -> X
            activate(n__c()) -> c()
            activate(n__d()) -> d()
            c() -> d()
            c() -> n__c()
            d() -> n__d()
        - Signature:
            {activate/1,c/0,d/0,g/1,h/1,activate#/1,c#/0,d#/0,g#/1,h#/1} / {n__c/0,n__d/0,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
            ,c_6/0,c_7/2,c_8/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,d#,g#,h#} and constructors {n__c,n__d}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:g#(X) -> c_7(h#(activate(X)),activate#(X))
             -->_1 h#(n__d()) -> c_8(g#(n__c())):2
          
          2:S:h#(n__d()) -> c_8(g#(n__c()))
             -->_1 g#(X) -> c_7(h#(activate(X)),activate#(X)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          g#(X) -> c_7(h#(activate(X)))
* Step 8: WeightGap MAYBE
    + Considered Problem:
        - Strict DPs:
            g#(X) -> c_7(h#(activate(X)))
            h#(n__d()) -> c_8(g#(n__c()))
        - Weak TRS:
            activate(X) -> X
            activate(n__c()) -> c()
            activate(n__d()) -> d()
            c() -> d()
            c() -> n__c()
            d() -> n__d()
        - Signature:
            {activate/1,c/0,d/0,g/1,h/1,activate#/1,c#/0,d#/0,g#/1,h#/1} / {n__c/0,n__d/0,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
            ,c_6/0,c_7/1,c_8/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,c#,d#,g#,h#} and constructors {n__c,n__d}
    + 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(h#) = {1},
            uargs(c_7) = {1},
            uargs(c_8) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
             p(activate) = [9] x1 + [13]
                    p(c) = [2]          
                    p(d) = [2]          
                    p(g) = [0]          
                    p(h) = [0]          
                 p(n__c) = [0]          
                 p(n__d) = [2]          
            p(activate#) = [0]          
                   p(c#) = [0]          
                   p(d#) = [0]          
                   p(g#) = [9] x1 + [2] 
                   p(h#) = [1] x1 + [9] 
                  p(c_1) = [0]          
                  p(c_2) = [0]          
                  p(c_3) = [0]          
                  p(c_4) = [0]          
                  p(c_5) = [0]          
                  p(c_6) = [0]          
                  p(c_7) = [1] x1 + [0] 
                  p(c_8) = [1] x1 + [0] 
          
          Following rules are strictly oriented:
          h#(n__d()) = [11]           
                     > [2]            
                     = c_8(g#(n__c()))
          
          
          Following rules are (at-least) weakly oriented:
                     g#(X) =  [9] X + [2]         
                           >= [9] X + [22]        
                           =  c_7(h#(activate(X)))
          
               activate(X) =  [9] X + [13]        
                           >= [1] X + [0]         
                           =  X                   
          
          activate(n__c()) =  [13]                
                           >= [2]                 
                           =  c()                 
          
          activate(n__d()) =  [31]                
                           >= [2]                 
                           =  d()                 
          
                       c() =  [2]                 
                           >= [2]                 
                           =  d()                 
          
                       c() =  [2]                 
                           >= [0]                 
                           =  n__c()              
          
                       d() =  [2]                 
                           >= [2]                 
                           =  n__d()              
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 9: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          g#(X) -> c_7(h#(activate(X)))
      - Weak DPs:
          h#(n__d()) -> c_8(g#(n__c()))
      - Weak TRS:
          activate(X) -> X
          activate(n__c()) -> c()
          activate(n__d()) -> d()
          c() -> d()
          c() -> n__c()
          d() -> n__d()
      - Signature:
          {activate/1,c/0,d/0,g/1,h/1,activate#/1,c#/0,d#/0,g#/1,h#/1} / {n__c/0,n__d/0,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0
          ,c_6/0,c_7/1,c_8/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,c#,d#,g#,h#} and constructors {n__c,n__d}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE