WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            addlist(Cons(x,xs'),Cons(S(0()),xs)) -> Cons(S(x),addlist(xs',xs))
            addlist(Cons(S(0()),xs'),Cons(x,xs)) -> Cons(S(x),addlist(xs',xs))
            addlist(Nil(),ys) -> Nil()
            goal(xs,ys) -> addlist(xs,ys)
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
        - Signature:
            {addlist/2,goal/2,notEmpty/1} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {addlist,goal,notEmpty} and constructors {0,Cons,False,Nil
            ,S,True}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(Cons) = {2}
        
        Following symbols are considered usable:
          {addlist,goal,notEmpty}
        TcT has computed the following interpretation:
                 p(0) = [1]                  
              p(Cons) = [1] x2 + [4]         
             p(False) = [3]                  
               p(Nil) = [4]                  
                 p(S) = [4]                  
              p(True) = [9]                  
           p(addlist) = [4] x1 + [0]         
              p(goal) = [8] x1 + [2] x2 + [2]
          p(notEmpty) = [2] x1 + [7]         
        
        Following rules are strictly oriented:
        addlist(Cons(x,xs'),Cons(S(0()),xs)) = [4] xs' + [16]            
                                             > [4] xs' + [4]             
                                             = Cons(S(x),addlist(xs',xs))
        
        addlist(Cons(S(0()),xs'),Cons(x,xs)) = [4] xs' + [16]            
                                             > [4] xs' + [4]             
                                             = Cons(S(x),addlist(xs',xs))
        
                           addlist(Nil(),ys) = [16]                      
                                             > [4]                       
                                             = Nil()                     
        
                                 goal(xs,ys) = [8] xs + [2] ys + [2]     
                                             > [4] xs + [0]              
                                             = addlist(xs,ys)            
        
                        notEmpty(Cons(x,xs)) = [2] xs + [15]             
                                             > [9]                       
                                             = True()                    
        
                             notEmpty(Nil()) = [15]                      
                                             > [3]                       
                                             = False()                   
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))