WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__first(X1,X2)) -> first(X1,X2)
            activate(n__from(X)) -> from(X)
            first(X1,X2) -> n__first(X1,X2)
            first(0(),X) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {activate/1,first/2,from/1} / {0/0,cons/2,n__first/2,n__from/1,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,first,from} and constructors {0,cons,n__first
            ,n__from,nil,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(cons) = {2},
          uargs(n__first) = {2}
        
        Following symbols are considered usable:
          {activate,first,from}
        TcT has computed the following interpretation:
                 p(0) = [0]                  
          p(activate) = [4] x1 + [10]        
              p(cons) = [1] x2 + [4]         
             p(first) = [3] x1 + [4] x2 + [4]
              p(from) = [4] x1 + [9]         
          p(n__first) = [1] x1 + [1] x2 + [0]
           p(n__from) = [1] x1 + [1]         
               p(nil) = [0]                  
                 p(s) = [1] x1 + [3]         
        
        Following rules are strictly oriented:
                      activate(X) = [4] X + [10]                   
                                  > [1] X + [0]                    
                                  = X                              
        
        activate(n__first(X1,X2)) = [4] X1 + [4] X2 + [10]         
                                  > [3] X1 + [4] X2 + [4]          
                                  = first(X1,X2)                   
        
             activate(n__from(X)) = [4] X + [14]                   
                                  > [4] X + [9]                    
                                  = from(X)                        
        
                     first(X1,X2) = [3] X1 + [4] X2 + [4]          
                                  > [1] X1 + [1] X2 + [0]          
                                  = n__first(X1,X2)                
        
                     first(0(),X) = [4] X + [4]                    
                                  > [0]                            
                                  = nil()                          
        
            first(s(X),cons(Y,Z)) = [3] X + [4] Z + [29]           
                                  > [1] X + [4] Z + [14]           
                                  = cons(Y,n__first(X,activate(Z)))
        
                          from(X) = [4] X + [9]                    
                                  > [1] X + [8]                    
                                  = cons(X,n__from(s(X)))          
        
                          from(X) = [4] X + [9]                    
                                  > [1] X + [1]                    
                                  = n__from(X)                     
        
        
        Following rules are (at-least) weakly oriented:
        
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            activate(X) -> X
            activate(n__first(X1,X2)) -> first(X1,X2)
            activate(n__from(X)) -> from(X)
            first(X1,X2) -> n__first(X1,X2)
            first(0(),X) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {activate/1,first/2,from/1} / {0/0,cons/2,n__first/2,n__from/1,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,first,from} and constructors {0,cons,n__first
            ,n__from,nil,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))