*** 1 Progress [(?,O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
        2nd(cons1(X,cons(Y,Z))) -> Y
        activate(X) -> X
        activate(n__from(X)) -> from(activate(X))
        activate(n__s(X)) -> s(activate(X))
        from(X) -> cons(X,n__from(n__s(X)))
        from(X) -> n__from(X)
        s(X) -> n__s(X)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {2nd/1,activate/1,from/1,s/1} / {cons/2,cons1/2,n__from/1,n__s/1}
      Obligation:
        Innermost
        basic terms: {2nd,activate,from,s}/{cons,cons1,n__from,n__s}
    Applied Processor:
      DependencyPairs {dpKind_ = DT}
    Proof:
      We add the following dependency tuples:
      
      Strict DPs
        2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
        2nd#(cons1(X,cons(Y,Z))) -> c_2()
        activate#(X) -> c_3()
        activate#(n__from(X)) -> c_4(from#(activate(X)),activate#(X))
        activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
        from#(X) -> c_6()
        from#(X) -> c_7()
        s#(X) -> c_8()
      Weak DPs
        
      
      and mark the set of starting terms.
*** 1.1 Progress [(?,O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
        2nd#(cons1(X,cons(Y,Z))) -> c_2()
        activate#(X) -> c_3()
        activate#(n__from(X)) -> c_4(from#(activate(X)),activate#(X))
        activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
        from#(X) -> c_6()
        from#(X) -> c_7()
        s#(X) -> c_8()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
        2nd(cons1(X,cons(Y,Z))) -> Y
        activate(X) -> X
        activate(n__from(X)) -> from(activate(X))
        activate(n__s(X)) -> s(activate(X))
        from(X) -> cons(X,n__from(n__s(X)))
        from(X) -> n__from(X)
        s(X) -> n__s(X)
      Signature:
        {2nd/1,activate/1,from/1,s/1,2nd#/1,activate#/1,from#/1,s#/1} / {cons/2,cons1/2,n__from/1,n__s/1,c_1/2,c_2/0,c_3/0,c_4/2,c_5/2,c_6/0,c_7/0,c_8/0}
      Obligation:
        Innermost
        basic terms: {2nd#,activate#,from#,s#}/{cons,cons1,n__from,n__s}
    Applied Processor:
      UsableRules
    Proof:
      We replace rewrite rules by usable rules:
        activate(X) -> X
        activate(n__from(X)) -> from(activate(X))
        activate(n__s(X)) -> s(activate(X))
        from(X) -> cons(X,n__from(n__s(X)))
        from(X) -> n__from(X)
        s(X) -> n__s(X)
        2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
        2nd#(cons1(X,cons(Y,Z))) -> c_2()
        activate#(X) -> c_3()
        activate#(n__from(X)) -> c_4(from#(activate(X)),activate#(X))
        activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
        from#(X) -> c_6()
        from#(X) -> c_7()
        s#(X) -> c_8()
*** 1.1.1 Progress [(?,O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
        2nd#(cons1(X,cons(Y,Z))) -> c_2()
        activate#(X) -> c_3()
        activate#(n__from(X)) -> c_4(from#(activate(X)),activate#(X))
        activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
        from#(X) -> c_6()
        from#(X) -> c_7()
        s#(X) -> c_8()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        activate(X) -> X
        activate(n__from(X)) -> from(activate(X))
        activate(n__s(X)) -> s(activate(X))
        from(X) -> cons(X,n__from(n__s(X)))
        from(X) -> n__from(X)
        s(X) -> n__s(X)
      Signature:
        {2nd/1,activate/1,from/1,s/1,2nd#/1,activate#/1,from#/1,s#/1} / {cons/2,cons1/2,n__from/1,n__s/1,c_1/2,c_2/0,c_3/0,c_4/2,c_5/2,c_6/0,c_7/0,c_8/0}
      Obligation:
        Innermost
        basic terms: {2nd#,activate#,from#,s#}/{cons,cons1,n__from,n__s}
    Applied Processor:
      PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    Proof:
      We estimate the number of application of
        {2,3,6,7,8}
      by application of
        Pre({2,3,6,7,8}) = {1,4,5}.
      Here rules are labelled as follows:
        1: 2nd#(cons(X,X1)) ->              
             c_1(2nd#(cons1(X,activate(X1)))
                ,activate#(X1))             
        2: 2nd#(cons1(X,cons(Y,Z))) ->      
             c_2()                          
        3: activate#(X) -> c_3()            
        4: activate#(n__from(X)) ->         
             c_4(from#(activate(X))         
                ,activate#(X))              
        5: activate#(n__s(X)) ->            
             c_5(s#(activate(X))            
                ,activate#(X))              
        6: from#(X) -> c_6()                
        7: from#(X) -> c_7()                
        8: s#(X) -> c_8()                   
*** 1.1.1.1 Progress [(?,O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
        activate#(n__from(X)) -> c_4(from#(activate(X)),activate#(X))
        activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
      Strict TRS Rules:
        
      Weak DP Rules:
        2nd#(cons1(X,cons(Y,Z))) -> c_2()
        activate#(X) -> c_3()
        from#(X) -> c_6()
        from#(X) -> c_7()
        s#(X) -> c_8()
      Weak TRS Rules:
        activate(X) -> X
        activate(n__from(X)) -> from(activate(X))
        activate(n__s(X)) -> s(activate(X))
        from(X) -> cons(X,n__from(n__s(X)))
        from(X) -> n__from(X)
        s(X) -> n__s(X)
      Signature:
        {2nd/1,activate/1,from/1,s/1,2nd#/1,activate#/1,from#/1,s#/1} / {cons/2,cons1/2,n__from/1,n__s/1,c_1/2,c_2/0,c_3/0,c_4/2,c_5/2,c_6/0,c_7/0,c_8/0}
      Obligation:
        Innermost
        basic terms: {2nd#,activate#,from#,s#}/{cons,cons1,n__from,n__s}
    Applied Processor:
      RemoveWeakSuffixes
    Proof:
      Consider the dependency graph
        1:S:2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
           -->_2 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
           -->_2 activate#(n__from(X)) -> c_4(from#(activate(X)),activate#(X)):2
           -->_2 activate#(X) -> c_3():5
           -->_1 2nd#(cons1(X,cons(Y,Z))) -> c_2():4
        
        2:S:activate#(n__from(X)) -> c_4(from#(activate(X)),activate#(X))
           -->_2 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
           -->_1 from#(X) -> c_7():7
           -->_1 from#(X) -> c_6():6
           -->_2 activate#(X) -> c_3():5
           -->_2 activate#(n__from(X)) -> c_4(from#(activate(X)),activate#(X)):2
        
        3:S:activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
           -->_1 s#(X) -> c_8():8
           -->_2 activate#(X) -> c_3():5
           -->_2 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
           -->_2 activate#(n__from(X)) -> c_4(from#(activate(X)),activate#(X)):2
        
        4:W:2nd#(cons1(X,cons(Y,Z))) -> c_2()
           
        
        5:W:activate#(X) -> c_3()
           
        
        6:W:from#(X) -> c_6()
           
        
        7:W:from#(X) -> c_7()
           
        
        8:W:s#(X) -> c_8()
           
        
      The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
        4: 2nd#(cons1(X,cons(Y,Z))) ->
             c_2()                    
        6: from#(X) -> c_6()          
        7: from#(X) -> c_7()          
        5: activate#(X) -> c_3()      
        8: s#(X) -> c_8()             
*** 1.1.1.1.1 Progress [(?,O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
        activate#(n__from(X)) -> c_4(from#(activate(X)),activate#(X))
        activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        activate(X) -> X
        activate(n__from(X)) -> from(activate(X))
        activate(n__s(X)) -> s(activate(X))
        from(X) -> cons(X,n__from(n__s(X)))
        from(X) -> n__from(X)
        s(X) -> n__s(X)
      Signature:
        {2nd/1,activate/1,from/1,s/1,2nd#/1,activate#/1,from#/1,s#/1} / {cons/2,cons1/2,n__from/1,n__s/1,c_1/2,c_2/0,c_3/0,c_4/2,c_5/2,c_6/0,c_7/0,c_8/0}
      Obligation:
        Innermost
        basic terms: {2nd#,activate#,from#,s#}/{cons,cons1,n__from,n__s}
    Applied Processor:
      SimplifyRHS
    Proof:
      Consider the dependency graph
        1:S:2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
           -->_2 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
           -->_2 activate#(n__from(X)) -> c_4(from#(activate(X)),activate#(X)):2
        
        2:S:activate#(n__from(X)) -> c_4(from#(activate(X)),activate#(X))
           -->_2 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
           -->_2 activate#(n__from(X)) -> c_4(from#(activate(X)),activate#(X)):2
        
        3:S:activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
           -->_2 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
           -->_2 activate#(n__from(X)) -> c_4(from#(activate(X)),activate#(X)):2
        
      Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
        2nd#(cons(X,X1)) -> c_1(activate#(X1))
        activate#(n__from(X)) -> c_4(activate#(X))
        activate#(n__s(X)) -> c_5(activate#(X))
*** 1.1.1.1.1.1 Progress [(?,O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        2nd#(cons(X,X1)) -> c_1(activate#(X1))
        activate#(n__from(X)) -> c_4(activate#(X))
        activate#(n__s(X)) -> c_5(activate#(X))
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        activate(X) -> X
        activate(n__from(X)) -> from(activate(X))
        activate(n__s(X)) -> s(activate(X))
        from(X) -> cons(X,n__from(n__s(X)))
        from(X) -> n__from(X)
        s(X) -> n__s(X)
      Signature:
        {2nd/1,activate/1,from/1,s/1,2nd#/1,activate#/1,from#/1,s#/1} / {cons/2,cons1/2,n__from/1,n__s/1,c_1/1,c_2/0,c_3/0,c_4/1,c_5/1,c_6/0,c_7/0,c_8/0}
      Obligation:
        Innermost
        basic terms: {2nd#,activate#,from#,s#}/{cons,cons1,n__from,n__s}
    Applied Processor:
      UsableRules
    Proof:
      We replace rewrite rules by usable rules:
        2nd#(cons(X,X1)) -> c_1(activate#(X1))
        activate#(n__from(X)) -> c_4(activate#(X))
        activate#(n__s(X)) -> c_5(activate#(X))
*** 1.1.1.1.1.1.1 Progress [(?,O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        2nd#(cons(X,X1)) -> c_1(activate#(X1))
        activate#(n__from(X)) -> c_4(activate#(X))
        activate#(n__s(X)) -> c_5(activate#(X))
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {2nd/1,activate/1,from/1,s/1,2nd#/1,activate#/1,from#/1,s#/1} / {cons/2,cons1/2,n__from/1,n__s/1,c_1/1,c_2/0,c_3/0,c_4/1,c_5/1,c_6/0,c_7/0,c_8/0}
      Obligation:
        Innermost
        basic terms: {2nd#,activate#,from#,s#}/{cons,cons1,n__from,n__s}
    Applied Processor:
      RemoveHeads
    Proof:
      Consider the dependency graph
      
      1:S:2nd#(cons(X,X1)) -> c_1(activate#(X1))
         -->_1 activate#(n__s(X)) -> c_5(activate#(X)):3
         -->_1 activate#(n__from(X)) -> c_4(activate#(X)):2
      
      2:S:activate#(n__from(X)) -> c_4(activate#(X))
         -->_1 activate#(n__s(X)) -> c_5(activate#(X)):3
         -->_1 activate#(n__from(X)) -> c_4(activate#(X)):2
      
      3:S:activate#(n__s(X)) -> c_5(activate#(X))
         -->_1 activate#(n__s(X)) -> c_5(activate#(X)):3
         -->_1 activate#(n__from(X)) -> c_4(activate#(X)):2
      
      
      Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts).
      
      [(1,2nd#(cons(X,X1)) -> c_1(activate#(X1)))]
*** 1.1.1.1.1.1.1.1 Progress [(?,O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        activate#(n__from(X)) -> c_4(activate#(X))
        activate#(n__s(X)) -> c_5(activate#(X))
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {2nd/1,activate/1,from/1,s/1,2nd#/1,activate#/1,from#/1,s#/1} / {cons/2,cons1/2,n__from/1,n__s/1,c_1/1,c_2/0,c_3/0,c_4/1,c_5/1,c_6/0,c_7/0,c_8/0}
      Obligation:
        Innermost
        basic terms: {2nd#,activate#,from#,s#}/{cons,cons1,n__from,n__s}
    Applied Processor:
      PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing, greedy = NoGreedy}}
    Proof:
      We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing, greedy = NoGreedy} to orient following rules strictly:
        3: activate#(n__s(X)) ->
             c_5(activate#(X))  
        
      The strictly oriented rules are moved into the weak component.
  *** 1.1.1.1.1.1.1.1.1 Progress [(?,O(n^1))]  ***
      Considered Problem:
        Strict DP Rules:
          activate#(n__from(X)) -> c_4(activate#(X))
          activate#(n__s(X)) -> c_5(activate#(X))
        Strict TRS Rules:
          
        Weak DP Rules:
          
        Weak TRS Rules:
          
        Signature:
          {2nd/1,activate/1,from/1,s/1,2nd#/1,activate#/1,from#/1,s#/1} / {cons/2,cons1/2,n__from/1,n__s/1,c_1/1,c_2/0,c_3/0,c_4/1,c_5/1,c_6/0,c_7/0,c_8/0}
        Obligation:
          Innermost
          basic terms: {2nd#,activate#,from#,s#}/{cons,cons1,n__from,n__s}
      Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation any intersect of rules of CDG leaf and strict-rules, greedy = NoGreedy}
      Proof:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_4) = {1},
          uargs(c_5) = {1}
        
        Following symbols are considered usable:
          {2nd#,activate#,from#,s#}
        TcT has computed the following interpretation:
                p(2nd) = [1] x1 + [1]
           p(activate) = [1]         
               p(cons) = [1] x1 + [0]
              p(cons1) = [1] x2 + [1]
               p(from) = [1] x1 + [8]
            p(n__from) = [1] x1 + [0]
               p(n__s) = [1] x1 + [2]
                  p(s) = [1] x1 + [1]
               p(2nd#) = [1] x1 + [1]
          p(activate#) = [8] x1 + [0]
              p(from#) = [1]         
                 p(s#) = [0]         
                p(c_1) = [1] x1 + [0]
                p(c_2) = [1]         
                p(c_3) = [1]         
                p(c_4) = [1] x1 + [0]
                p(c_5) = [1] x1 + [6]
                p(c_6) = [0]         
                p(c_7) = [8]         
                p(c_8) = [2]         
        
        Following rules are strictly oriented:
        activate#(n__s(X)) = [8] X + [16]     
                           > [8] X + [6]      
                           = c_5(activate#(X))
        
        
        Following rules are (at-least) weakly oriented:
        activate#(n__from(X)) =  [8] X + [0]      
                              >= [8] X + [0]      
                              =  c_4(activate#(X))
        
  *** 1.1.1.1.1.1.1.1.1.1 Progress [(?,O(1))]  ***
      Considered Problem:
        Strict DP Rules:
          activate#(n__from(X)) -> c_4(activate#(X))
        Strict TRS Rules:
          
        Weak DP Rules:
          activate#(n__s(X)) -> c_5(activate#(X))
        Weak TRS Rules:
          
        Signature:
          {2nd/1,activate/1,from/1,s/1,2nd#/1,activate#/1,from#/1,s#/1} / {cons/2,cons1/2,n__from/1,n__s/1,c_1/1,c_2/0,c_3/0,c_4/1,c_5/1,c_6/0,c_7/0,c_8/0}
        Obligation:
          Innermost
          basic terms: {2nd#,activate#,from#,s#}/{cons,cons1,n__from,n__s}
      Applied Processor:
        Assumption
      Proof:
        ()
  
  *** 1.1.1.1.1.1.1.1.2 Progress [(?,O(n^1))]  ***
      Considered Problem:
        Strict DP Rules:
          activate#(n__from(X)) -> c_4(activate#(X))
        Strict TRS Rules:
          
        Weak DP Rules:
          activate#(n__s(X)) -> c_5(activate#(X))
        Weak TRS Rules:
          
        Signature:
          {2nd/1,activate/1,from/1,s/1,2nd#/1,activate#/1,from#/1,s#/1} / {cons/2,cons1/2,n__from/1,n__s/1,c_1/1,c_2/0,c_3/0,c_4/1,c_5/1,c_6/0,c_7/0,c_8/0}
        Obligation:
          Innermost
          basic terms: {2nd#,activate#,from#,s#}/{cons,cons1,n__from,n__s}
      Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing, greedy = NoGreedy}}
      Proof:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing, greedy = NoGreedy} to orient following rules strictly:
          1: activate#(n__from(X)) ->
               c_4(activate#(X))     
          
        The strictly oriented rules are moved into the weak component.
    *** 1.1.1.1.1.1.1.1.2.1 Progress [(?,O(n^1))]  ***
        Considered Problem:
          Strict DP Rules:
            activate#(n__from(X)) -> c_4(activate#(X))
          Strict TRS Rules:
            
          Weak DP Rules:
            activate#(n__s(X)) -> c_5(activate#(X))
          Weak TRS Rules:
            
          Signature:
            {2nd/1,activate/1,from/1,s/1,2nd#/1,activate#/1,from#/1,s#/1} / {cons/2,cons1/2,n__from/1,n__s/1,c_1/1,c_2/0,c_3/0,c_4/1,c_5/1,c_6/0,c_7/0,c_8/0}
          Obligation:
            Innermost
            basic terms: {2nd#,activate#,from#,s#}/{cons,cons1,n__from,n__s}
        Applied Processor:
          NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation any intersect of rules of CDG leaf and strict-rules, greedy = NoGreedy}
        Proof:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            uargs(c_4) = {1},
            uargs(c_5) = {1}
          
          Following symbols are considered usable:
            {2nd#,activate#,from#,s#}
          TcT has computed the following interpretation:
                  p(2nd) = [2] x1 + [1]
             p(activate) = [1]         
                 p(cons) = [0]         
                p(cons1) = [1] x2 + [1]
                 p(from) = [1]         
              p(n__from) = [1] x1 + [8]
                 p(n__s) = [1] x1 + [6]
                    p(s) = [8] x1 + [0]
                 p(2nd#) = [2] x1 + [2]
            p(activate#) = [1] x1 + [0]
                p(from#) = [4]         
                   p(s#) = [0]         
                  p(c_1) = [2] x1 + [1]
                  p(c_2) = [1]         
                  p(c_3) = [1]         
                  p(c_4) = [1] x1 + [0]
                  p(c_5) = [1] x1 + [0]
                  p(c_6) = [2]         
                  p(c_7) = [1]         
                  p(c_8) = [0]         
          
          Following rules are strictly oriented:
          activate#(n__from(X)) = [1] X + [8]      
                                > [1] X + [0]      
                                = c_4(activate#(X))
          
          
          Following rules are (at-least) weakly oriented:
          activate#(n__s(X)) =  [1] X + [6]      
                             >= [1] X + [0]      
                             =  c_5(activate#(X))
          
    *** 1.1.1.1.1.1.1.1.2.1.1 Progress [(?,O(1))]  ***
        Considered Problem:
          Strict DP Rules:
            
          Strict TRS Rules:
            
          Weak DP Rules:
            activate#(n__from(X)) -> c_4(activate#(X))
            activate#(n__s(X)) -> c_5(activate#(X))
          Weak TRS Rules:
            
          Signature:
            {2nd/1,activate/1,from/1,s/1,2nd#/1,activate#/1,from#/1,s#/1} / {cons/2,cons1/2,n__from/1,n__s/1,c_1/1,c_2/0,c_3/0,c_4/1,c_5/1,c_6/0,c_7/0,c_8/0}
          Obligation:
            Innermost
            basic terms: {2nd#,activate#,from#,s#}/{cons,cons1,n__from,n__s}
        Applied Processor:
          Assumption
        Proof:
          ()
    
    *** 1.1.1.1.1.1.1.1.2.2 Progress [(O(1),O(1))]  ***
        Considered Problem:
          Strict DP Rules:
            
          Strict TRS Rules:
            
          Weak DP Rules:
            activate#(n__from(X)) -> c_4(activate#(X))
            activate#(n__s(X)) -> c_5(activate#(X))
          Weak TRS Rules:
            
          Signature:
            {2nd/1,activate/1,from/1,s/1,2nd#/1,activate#/1,from#/1,s#/1} / {cons/2,cons1/2,n__from/1,n__s/1,c_1/1,c_2/0,c_3/0,c_4/1,c_5/1,c_6/0,c_7/0,c_8/0}
          Obligation:
            Innermost
            basic terms: {2nd#,activate#,from#,s#}/{cons,cons1,n__from,n__s}
        Applied Processor:
          RemoveWeakSuffixes
        Proof:
          Consider the dependency graph
            1:W:activate#(n__from(X)) -> c_4(activate#(X))
               -->_1 activate#(n__s(X)) -> c_5(activate#(X)):2
               -->_1 activate#(n__from(X)) -> c_4(activate#(X)):1
            
            2:W:activate#(n__s(X)) -> c_5(activate#(X))
               -->_1 activate#(n__s(X)) -> c_5(activate#(X)):2
               -->_1 activate#(n__from(X)) -> c_4(activate#(X)):1
            
          The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
            1: activate#(n__from(X)) ->
                 c_4(activate#(X))     
            2: activate#(n__s(X)) ->   
                 c_5(activate#(X))     
    *** 1.1.1.1.1.1.1.1.2.2.1 Progress [(O(1),O(1))]  ***
        Considered Problem:
          Strict DP Rules:
            
          Strict TRS Rules:
            
          Weak DP Rules:
            
          Weak TRS Rules:
            
          Signature:
            {2nd/1,activate/1,from/1,s/1,2nd#/1,activate#/1,from#/1,s#/1} / {cons/2,cons1/2,n__from/1,n__s/1,c_1/1,c_2/0,c_3/0,c_4/1,c_5/1,c_6/0,c_7/0,c_8/0}
          Obligation:
            Innermost
            basic terms: {2nd#,activate#,from#,s#}/{cons,cons1,n__from,n__s}
        Applied Processor:
          EmptyProcessor
        Proof:
          The problem is already closed. The intended complexity is O(1).