WORST_CASE(?,O(n^1))
* Step 1: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            goal(xs) -> ordered(xs)
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            ordered(Cons(x,Nil())) -> True()
            ordered(Cons(x',Cons(x,xs))) -> ordered[Ite](<(x',x),Cons(x',Cons(x,xs)))
            ordered(Nil()) -> True()
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            ordered[Ite](False(),xs) -> False()
            ordered[Ite](True(),Cons(x,xs)) -> ordered(xs)
        - Signature:
            {</2,goal/1,notEmpty/1,ordered/1,ordered[Ite]/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {<,goal,notEmpty,ordered,ordered[Ite]} 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(ordered[Ite]) = {1}
        
        Following symbols are considered usable:
          {<,goal,notEmpty,ordered,ordered[Ite]}
        TcT has computed the following interpretation:
                     p(0) = 1      
                     p(<) = 0      
                  p(Cons) = 7 + x2 
                 p(False) = 0      
                   p(Nil) = 11     
                     p(S) = 1 + x1 
                  p(True) = 0      
                  p(goal) = 8 + x1 
              p(notEmpty) = 13 + x1
               p(ordered) = 2 + x1 
          p(ordered[Ite]) = x1 + x2
        
        Following rules are strictly oriented:
                            goal(xs) = 8 + xs                                   
                                     > 2 + xs                                   
                                     = ordered(xs)                              
        
                notEmpty(Cons(x,xs)) = 20 + xs                                  
                                     > 0                                        
                                     = True()                                   
        
                     notEmpty(Nil()) = 24                                       
                                     > 0                                        
                                     = False()                                  
        
              ordered(Cons(x,Nil())) = 20                                       
                                     > 0                                        
                                     = True()                                   
        
        ordered(Cons(x',Cons(x,xs))) = 16 + xs                                  
                                     > 14 + xs                                  
                                     = ordered[Ite](<(x',x),Cons(x',Cons(x,xs)))
        
                      ordered(Nil()) = 13                                       
                                     > 0                                        
                                     = True()                                   
        
        
        Following rules are (at-least) weakly oriented:
                               <(x,0()) =  0          
                                        >= 0          
                                        =  False()    
        
                            <(0(),S(y)) =  0          
                                        >= 0          
                                        =  True()     
        
                           <(S(x),S(y)) =  0          
                                        >= 0          
                                        =  <(x,y)     
        
               ordered[Ite](False(),xs) =  xs         
                                        >= 0          
                                        =  False()    
        
        ordered[Ite](True(),Cons(x,xs)) =  7 + xs     
                                        >= 2 + xs     
                                        =  ordered(xs)
        

WORST_CASE(?,O(n^1))