* Step 1: MI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from,s}
    + Applied Processor:
        MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity Nothing)), miDimension = 1, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity Nothing)):
        
        The following argument positions are considered usable:
          none
        
        Following symbols are considered usable:
          all
        TcT has computed the following interpretation:
               p(2nd) = [2] x_1 + [3]          
          p(activate) = [8] x_1 + [10]         
              p(cons) = [1] x_1 + [8] x_2 + [4]
              p(from) = [1] x_1 + [4]          
           p(n__cons) = [1] x_1 + [1] x_2 + [0]
           p(n__from) = [1] x_1 + [0]          
                 p(s) = [0]                    
        
        Following rules are strictly oriented:
        2nd(cons(X,n__cons(Y,Z))) = [2] X + [16] Y + [16] Z + [11]
                                  > [8] Y + [10]                  
                                  = activate(Y)                   
        
                      activate(X) = [8] X + [10]                  
                                  > [1] X + [0]                   
                                  = X                             
        
         activate(n__cons(X1,X2)) = [8] X1 + [8] X2 + [10]        
                                  > [1] X1 + [8] X2 + [4]         
                                  = cons(X1,X2)                   
        
             activate(n__from(X)) = [8] X + [10]                  
                                  > [1] X + [4]                   
                                  = from(X)                       
        
                      cons(X1,X2) = [1] X1 + [8] X2 + [4]         
                                  > [1] X1 + [1] X2 + [0]         
                                  = n__cons(X1,X2)                
        
                          from(X) = [1] X + [4]                   
                                  > [1] X + [0]                   
                                  = n__from(X)                    
        
        
        Following rules are (at-least) weakly oriented:
        from(X) =  [1] X + [4]          
                >= [1] X + [4]          
                =  cons(X,n__from(s(X)))
        
* Step 2: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            from(X) -> cons(X,n__from(s(X)))
        - Weak TRS:
            2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from,s}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following nonconstant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            none
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                 p(2nd) = [9] x1 + [7]         
            p(activate) = [8] x1 + [1]         
                p(cons) = [4] x1 + [2] x2 + [1]
                p(from) = [8] x1 + [15]        
             p(n__cons) = [1] x1 + [1] x2 + [0]
             p(n__from) = [1] x1 + [2]         
                   p(s) = [0]                  
          
          Following rules are strictly oriented:
          from(X) = [8] X + [15]         
                  > [4] X + [5]          
                  = cons(X,n__from(s(X)))
          
          
          Following rules are (at-least) weakly oriented:
          2nd(cons(X,n__cons(Y,Z))) =  [36] X + [18] Y + [18] Z + [16]
                                    >= [8] Y + [1]                    
                                    =  activate(Y)                    
          
                        activate(X) =  [8] X + [1]                    
                                    >= [1] X + [0]                    
                                    =  X                              
          
           activate(n__cons(X1,X2)) =  [8] X1 + [8] X2 + [1]          
                                    >= [4] X1 + [2] X2 + [1]          
                                    =  cons(X1,X2)                    
          
               activate(n__from(X)) =  [8] X + [17]                   
                                    >= [8] X + [15]                   
                                    =  from(X)                        
          
                        cons(X1,X2) =  [4] X1 + [2] X2 + [1]          
                                    >= [1] X1 + [1] X2 + [0]          
                                    =  n__cons(X1,X2)                 
          
                            from(X) =  [8] X + [15]                   
                                    >= [1] X + [2]                    
                                    =  n__from(X)                     
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))