/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(?,O(n^1))
* Step 1: Sum.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1} / {cons/2,cons1/2,n__from/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,activate,from} and constructors {cons,cons1,n__from,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1} / {cons/2,cons1/2,n__from/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,activate,from} and constructors {cons,cons1,n__from,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = WIDP}
    + Details:
        We add the following weak dependency pairs:
        
        Strict DPs
          2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))))
          2nd#(cons1(X,cons(Y,Z))) -> c_2(Y)
          activate#(X) -> c_3(X)
          activate#(n__from(X)) -> c_4(from#(X))
          from#(X) -> c_5(X,X)
          from#(X) -> c_6(X)
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: UsableRules.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))))
            2nd#(cons1(X,cons(Y,Z))) -> c_2(Y)
            activate#(X) -> c_3(X)
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_5(X,X)
            from#(X) -> c_6(X)
        - Strict TRS:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/1,c_2/1,c_3/1,c_4/1
            ,c_5/2,c_6/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1,n__from,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate(X) -> X
          activate(n__from(X)) -> from(X)
          from(X) -> cons(X,n__from(s(X)))
          from(X) -> n__from(X)
          2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))))
          2nd#(cons1(X,cons(Y,Z))) -> c_2(Y)
          activate#(X) -> c_3(X)
          activate#(n__from(X)) -> c_4(from#(X))
          from#(X) -> c_5(X,X)
          from#(X) -> c_6(X)
* Step 4: WeightGap.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))))
            2nd#(cons1(X,cons(Y,Z))) -> c_2(Y)
            activate#(X) -> c_3(X)
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_5(X,X)
            from#(X) -> c_6(X)
        - Strict TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/1,c_2/1,c_3/1,c_4/1
            ,c_5/2,c_6/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1,n__from,s}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnTrs}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            uargs(cons1) = {2},
            uargs(2nd#) = {1},
            uargs(c_1) = {1},
            uargs(c_4) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                  p(2nd) = [0]          
             p(activate) = [1] x1 + [15]
                 p(cons) = [1] x2 + [5] 
                p(cons1) = [1] x2 + [0] 
                 p(from) = [1] x1 + [6] 
              p(n__from) = [1] x1 + [0] 
                    p(s) = [1] x1 + [0] 
                 p(2nd#) = [1] x1 + [0] 
            p(activate#) = [0]          
                p(from#) = [0]          
                  p(c_1) = [1] x1 + [0] 
                  p(c_2) = [0]          
                  p(c_3) = [0]          
                  p(c_4) = [1] x1 + [0] 
                  p(c_5) = [0]          
                  p(c_6) = [0]          
          
          Following rules are strictly oriented:
          2nd#(cons1(X,cons(Y,Z))) = [1] Z + [5]          
                                   > [0]                  
                                   = c_2(Y)               
          
                       activate(X) = [1] X + [15]         
                                   > [1] X + [0]          
                                   = X                    
          
              activate(n__from(X)) = [1] X + [15]         
                                   > [1] X + [6]          
                                   = from(X)              
          
                           from(X) = [1] X + [6]          
                                   > [1] X + [5]          
                                   = cons(X,n__from(s(X)))
          
                           from(X) = [1] X + [6]          
                                   > [1] X + [0]          
                                   = n__from(X)           
          
          
          Following rules are (at-least) weakly oriented:
               2nd#(cons(X,X1)) =  [1] X1 + [5]                    
                                >= [1] X1 + [15]                   
                                =  c_1(2nd#(cons1(X,activate(X1))))
          
                   activate#(X) =  [0]                             
                                >= [0]                             
                                =  c_3(X)                          
          
          activate#(n__from(X)) =  [0]                             
                                >= [0]                             
                                =  c_4(from#(X))                   
          
                       from#(X) =  [0]                             
                                >= [0]                             
                                =  c_5(X,X)                        
          
                       from#(X) =  [0]                             
                                >= [0]                             
                                =  c_6(X)                          
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 5: PredecessorEstimationCP.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))))
            activate#(X) -> c_3(X)
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_5(X,X)
            from#(X) -> c_6(X)
        - Weak DPs:
            2nd#(cons1(X,cons(Y,Z))) -> c_2(Y)
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/1,c_2/1,c_3/1,c_4/1
            ,c_5/2,c_6/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1,n__from,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}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          2: activate#(X) -> c_3(X)
          3: activate#(n__from(X)) -> c_4(from#(X))
          4: from#(X) -> c_5(X,X)
          5: from#(X) -> c_6(X)
          
        The strictly oriented rules are moved into the weak component.
** Step 5.a:1: NaturalMI.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))))
            activate#(X) -> c_3(X)
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_5(X,X)
            from#(X) -> c_6(X)
        - Weak DPs:
            2nd#(cons1(X,cons(Y,Z))) -> c_2(Y)
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/1,c_2/1,c_3/1,c_4/1
            ,c_5/2,c_6/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1,n__from,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_1) = {1},
          uargs(c_4) = {1}
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
                p(2nd) = [0]                  
           p(activate) = [8] x1 + [4]         
               p(cons) = [1] x1 + [12]        
              p(cons1) = [1] x1 + [1] x2 + [0]
               p(from) = [8] x1 + [12]        
            p(n__from) = [1] x1 + [1]         
                  p(s) = [1] x1 + [1]         
               p(2nd#) = [0]                  
          p(activate#) = [2] x1 + [8]         
              p(from#) = [2] x1 + [7]         
                p(c_1) = [2] x1 + [0]         
                p(c_2) = [0]                  
                p(c_3) = [1] x1 + [4]         
                p(c_4) = [1] x1 + [0]         
                p(c_5) = [1] x1 + [0]         
                p(c_6) = [2] x1 + [5]         
        
        Following rules are strictly oriented:
                 activate#(X) = [2] X + [8]  
                              > [1] X + [4]  
                              = c_3(X)       
        
        activate#(n__from(X)) = [2] X + [10] 
                              > [2] X + [7]  
                              = c_4(from#(X))
        
                     from#(X) = [2] X + [7]  
                              > [1] X + [0]  
                              = c_5(X,X)     
        
                     from#(X) = [2] X + [7]  
                              > [2] X + [5]  
                              = c_6(X)       
        
        
        Following rules are (at-least) weakly oriented:
                2nd#(cons(X,X1)) =  [0]                             
                                 >= [0]                             
                                 =  c_1(2nd#(cons1(X,activate(X1))))
        
        2nd#(cons1(X,cons(Y,Z))) =  [0]                             
                                 >= [0]                             
                                 =  c_2(Y)                          
        
                     activate(X) =  [8] X + [4]                     
                                 >= [1] X + [0]                     
                                 =  X                               
        
            activate(n__from(X)) =  [8] X + [12]                    
                                 >= [8] X + [12]                    
                                 =  from(X)                         
        
                         from(X) =  [8] X + [12]                    
                                 >= [1] X + [12]                    
                                 =  cons(X,n__from(s(X)))           
        
                         from(X) =  [8] X + [12]                    
                                 >= [1] X + [1]                     
                                 =  n__from(X)                      
        
** Step 5.a:2: Assumption.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))))
        - Weak DPs:
            2nd#(cons1(X,cons(Y,Z))) -> c_2(Y)
            activate#(X) -> c_3(X)
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_5(X,X)
            from#(X) -> c_6(X)
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/1,c_2/1,c_3/1,c_4/1
            ,c_5/2,c_6/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1,n__from,s}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown, timeBCUB = Unknown, timeBCLB = Unknown}}
    + Details:
        ()

** Step 5.b:1: PredecessorEstimationCP.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))))
        - Weak DPs:
            2nd#(cons1(X,cons(Y,Z))) -> c_2(Y)
            activate#(X) -> c_3(X)
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_5(X,X)
            from#(X) -> c_6(X)
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/1,c_2/1,c_3/1,c_4/1
            ,c_5/2,c_6/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1,n__from,s}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: 2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))))
          
        The strictly oriented rules are moved into the weak component.
*** Step 5.b:1.a:1: NaturalMI.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))))
        - Weak DPs:
            2nd#(cons1(X,cons(Y,Z))) -> c_2(Y)
            activate#(X) -> c_3(X)
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_5(X,X)
            from#(X) -> c_6(X)
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/1,c_2/1,c_3/1,c_4/1
            ,c_5/2,c_6/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1,n__from,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        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_1) = {1},
          uargs(c_4) = {1}
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
                p(2nd) = [0]          
           p(activate) = [1] x1 + [5] 
               p(cons) = [8]          
              p(cons1) = [0]          
               p(from) = [8]          
            p(n__from) = [3]          
                  p(s) = [1]          
               p(2nd#) = [2] x1 + [0] 
          p(activate#) = [6] x1 + [2] 
              p(from#) = [0]          
                p(c_1) = [2] x1 + [15]
                p(c_2) = [0]          
                p(c_3) = [1] x1 + [1] 
                p(c_4) = [2] x1 + [8] 
                p(c_5) = [0]          
                p(c_6) = [0]          
        
        Following rules are strictly oriented:
        2nd#(cons(X,X1)) = [16]                            
                         > [15]                            
                         = c_1(2nd#(cons1(X,activate(X1))))
        
        
        Following rules are (at-least) weakly oriented:
        2nd#(cons1(X,cons(Y,Z))) =  [0]                  
                                 >= [0]                  
                                 =  c_2(Y)               
        
                    activate#(X) =  [6] X + [2]          
                                 >= [1] X + [1]          
                                 =  c_3(X)               
        
           activate#(n__from(X)) =  [20]                 
                                 >= [8]                  
                                 =  c_4(from#(X))        
        
                        from#(X) =  [0]                  
                                 >= [0]                  
                                 =  c_5(X,X)             
        
                        from#(X) =  [0]                  
                                 >= [0]                  
                                 =  c_6(X)               
        
                     activate(X) =  [1] X + [5]          
                                 >= [1] X + [0]          
                                 =  X                    
        
            activate(n__from(X)) =  [8]                  
                                 >= [8]                  
                                 =  from(X)              
        
                         from(X) =  [8]                  
                                 >= [8]                  
                                 =  cons(X,n__from(s(X)))
        
                         from(X) =  [8]                  
                                 >= [3]                  
                                 =  n__from(X)           
        
*** Step 5.b:1.a:2: Assumption.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))))
            2nd#(cons1(X,cons(Y,Z))) -> c_2(Y)
            activate#(X) -> c_3(X)
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_5(X,X)
            from#(X) -> c_6(X)
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/1,c_2/1,c_3/1,c_4/1
            ,c_5/2,c_6/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1,n__from,s}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown, timeBCUB = Unknown, timeBCLB = Unknown}}
    + Details:
        ()

*** Step 5.b:1.b:1: RemoveWeakSuffixes.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))))
            2nd#(cons1(X,cons(Y,Z))) -> c_2(Y)
            activate#(X) -> c_3(X)
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_5(X,X)
            from#(X) -> c_6(X)
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/1,c_2/1,c_3/1,c_4/1
            ,c_5/2,c_6/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1,n__from,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))))
             -->_1 2nd#(cons1(X,cons(Y,Z))) -> c_2(Y):2
          
          2:W:2nd#(cons1(X,cons(Y,Z))) -> c_2(Y)
             -->_1 from#(X) -> c_6(X):6
             -->_1 from#(X) -> c_5(X,X):5
             -->_1 activate#(n__from(X)) -> c_4(from#(X)):4
             -->_1 activate#(X) -> c_3(X):3
             -->_1 2nd#(cons1(X,cons(Y,Z))) -> c_2(Y):2
             -->_1 2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1)))):1
          
          3:W:activate#(X) -> c_3(X)
             -->_1 from#(X) -> c_6(X):6
             -->_1 from#(X) -> c_5(X,X):5
             -->_1 activate#(n__from(X)) -> c_4(from#(X)):4
             -->_1 activate#(X) -> c_3(X):3
             -->_1 2nd#(cons1(X,cons(Y,Z))) -> c_2(Y):2
             -->_1 2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1)))):1
          
          4:W:activate#(n__from(X)) -> c_4(from#(X))
             -->_1 from#(X) -> c_6(X):6
             -->_1 from#(X) -> c_5(X,X):5
          
          5:W:from#(X) -> c_5(X,X)
             -->_2 from#(X) -> c_6(X):6
             -->_1 from#(X) -> c_6(X):6
             -->_2 from#(X) -> c_5(X,X):5
             -->_1 from#(X) -> c_5(X,X):5
             -->_2 activate#(n__from(X)) -> c_4(from#(X)):4
             -->_1 activate#(n__from(X)) -> c_4(from#(X)):4
             -->_2 activate#(X) -> c_3(X):3
             -->_1 activate#(X) -> c_3(X):3
             -->_2 2nd#(cons1(X,cons(Y,Z))) -> c_2(Y):2
             -->_1 2nd#(cons1(X,cons(Y,Z))) -> c_2(Y):2
             -->_2 2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1)))):1
             -->_1 2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1)))):1
          
          6:W:from#(X) -> c_6(X)
             -->_1 from#(X) -> c_6(X):6
             -->_1 from#(X) -> c_5(X,X):5
             -->_1 activate#(n__from(X)) -> c_4(from#(X)):4
             -->_1 activate#(X) -> c_3(X):3
             -->_1 2nd#(cons1(X,cons(Y,Z))) -> c_2(Y):2
             -->_1 2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1)))):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: 2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))))
          6: from#(X) -> c_6(X)
          5: from#(X) -> c_5(X,X)
          4: activate#(n__from(X)) -> c_4(from#(X))
          3: activate#(X) -> c_3(X)
          2: 2nd#(cons1(X,cons(Y,Z))) -> c_2(Y)
*** Step 5.b:1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/1,c_2/1,c_3/1,c_4/1
            ,c_5/2,c_6/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1,n__from,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))