WORST_CASE(?,O(n^1))
* Step 1: NaturalPI 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:
        NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        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) = 10             
          p(activate) = 3 + 2*x1       
              p(cons) = 5 + x2         
             p(first) = 1 + 2*x1 + 2*x2
              p(from) = 14             
          p(n__first) = x1 + x2        
           p(n__from) = 8              
               p(nil) = 12             
                 p(s) = x1             
        
        Following rules are strictly oriented:
                      activate(X) = 3 + 2*X                        
                                  > X                              
                                  = X                              
        
        activate(n__first(X1,X2)) = 3 + 2*X1 + 2*X2                
                                  > 1 + 2*X1 + 2*X2                
                                  = first(X1,X2)                   
        
             activate(n__from(X)) = 19                             
                                  > 14                             
                                  = from(X)                        
        
                     first(X1,X2) = 1 + 2*X1 + 2*X2                
                                  > X1 + X2                        
                                  = n__first(X1,X2)                
        
                     first(0(),X) = 21 + 2*X                       
                                  > 12                             
                                  = nil()                          
        
            first(s(X),cons(Y,Z)) = 11 + 2*X + 2*Z                 
                                  > 8 + X + 2*Z                    
                                  = cons(Y,n__first(X,activate(Z)))
        
                          from(X) = 14                             
                                  > 13                             
                                  = cons(X,n__from(s(X)))          
        
                          from(X) = 14                             
                                  > 8                              
                                  = n__from(X)                     
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))