WORST_CASE(?,O(n^1))
* Step 1: NaturalPI 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:
        NaturalPI {shape = StronglyLinear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(stronglyLinear):
        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) = 8           
              p(Cons) = x1 + x2     
             p(False) = 1           
               p(Nil) = 2           
                 p(S) = 1 + x1      
              p(True) = 1           
           p(addlist) = 9 + x1 + x2 
              p(goal) = 14 + x1 + x2
          p(notEmpty) = 10          
        
        Following rules are strictly oriented:
        addlist(Cons(x,xs'),Cons(S(0()),xs)) = 18 + x + xs + xs'         
                                             > 10 + x + xs + xs'         
                                             = Cons(S(x),addlist(xs',xs))
        
        addlist(Cons(S(0()),xs'),Cons(x,xs)) = 18 + x + xs + xs'         
                                             > 10 + x + xs + xs'         
                                             = Cons(S(x),addlist(xs',xs))
        
                           addlist(Nil(),ys) = 11 + ys                   
                                             > 2                         
                                             = Nil()                     
        
                                 goal(xs,ys) = 14 + xs + ys              
                                             > 9 + xs + ys               
                                             = addlist(xs,ys)            
        
                        notEmpty(Cons(x,xs)) = 10                        
                                             > 1                         
                                             = True()                    
        
                             notEmpty(Nil()) = 10                        
                                             > 1                         
                                             = False()                   
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))