WORST_CASE(?,O(n^2))
* Step 1: NaturalPI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            loop(Cons(x,xs),Nil(),pp,ss) -> False()
            loop(Cons(x',xs'),Cons(x,xs),pp,ss) -> loop[Ite](!EQ(x',x),Cons(x',xs'),Cons(x,xs),pp,ss)
            loop(Nil(),s,pp,ss) -> True()
            match1(p,s) -> loop(p,s,p,s)
        - Weak TRS:
            !EQ(0(),0()) -> True()
            !EQ(0(),S(y)) -> False()
            !EQ(S(x),0()) -> False()
            !EQ(S(x),S(y)) -> !EQ(x,y)
            loop[Ite](False(),p,s,pp,Cons(x,xs)) -> loop(pp,xs,pp,xs)
            loop[Ite](True(),Cons(x',xs'),Cons(x,xs),pp,ss) -> loop(xs',xs,pp,ss)
        - Signature:
            {!EQ/2,loop/4,loop[Ite]/5,match1/2} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {!EQ,loop,loop[Ite],match1} and constructors {0,Cons,False
            ,Nil,S,True}
    + Applied Processor:
        NaturalPI {shape = Quadratic, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(quadratic):
        The following argument positions are considered usable:
          uargs(loop[Ite]) = {1}
        
        Following symbols are considered usable:
          {!EQ,loop,loop[Ite],match1}
        TcT has computed the following interpretation:
                p(!EQ) = 0                                 
                  p(0) = 0                                 
               p(Cons) = 2 + x2                            
              p(False) = 0                                 
                p(Nil) = 0                                 
                  p(S) = 1 + x1                            
               p(True) = 0                                 
               p(loop) = 1 + 5*x2 + 2*x3 + x3^2 + 2*x4^2   
          p(loop[Ite]) = 4*x1 + 5*x3 + 2*x4 + x4^2 + 2*x5^2
             p(match1) = 4 + 5*x1 + 6*x1^2 + 5*x2 + 4*x2^2 
        
        Following rules are strictly oriented:
               loop(Cons(x,xs),Nil(),pp,ss) = 1 + 2*pp + pp^2 + 2*ss^2                          
                                            > 0                                                 
                                            = False()                                           
        
        loop(Cons(x',xs'),Cons(x,xs),pp,ss) = 11 + 2*pp + pp^2 + 2*ss^2 + 5*xs                  
                                            > 10 + 2*pp + pp^2 + 2*ss^2 + 5*xs                  
                                            = loop[Ite](!EQ(x',x),Cons(x',xs'),Cons(x,xs),pp,ss)
        
                        loop(Nil(),s,pp,ss) = 1 + 2*pp + pp^2 + 5*s + 2*ss^2                    
                                            > 0                                                 
                                            = True()                                            
        
                                match1(p,s) = 4 + 5*p + 6*p^2 + 5*s + 4*s^2                     
                                            > 1 + 2*p + p^2 + 5*s + 2*s^2                       
                                            = loop(p,s,p,s)                                     
        
        
        Following rules are (at-least) weakly oriented:
                                           !EQ(0(),0()) =  0                                    
                                                        >= 0                                    
                                                        =  True()                               
        
                                          !EQ(0(),S(y)) =  0                                    
                                                        >= 0                                    
                                                        =  False()                              
        
                                          !EQ(S(x),0()) =  0                                    
                                                        >= 0                                    
                                                        =  False()                              
        
                                         !EQ(S(x),S(y)) =  0                                    
                                                        >= 0                                    
                                                        =  !EQ(x,y)                             
        
                   loop[Ite](False(),p,s,pp,Cons(x,xs)) =  8 + 2*pp + pp^2 + 5*s + 8*xs + 2*xs^2
                                                        >= 1 + 2*pp + pp^2 + 5*xs + 2*xs^2      
                                                        =  loop(pp,xs,pp,xs)                    
        
        loop[Ite](True(),Cons(x',xs'),Cons(x,xs),pp,ss) =  10 + 2*pp + pp^2 + 2*ss^2 + 5*xs     
                                                        >= 1 + 2*pp + pp^2 + 2*ss^2 + 5*xs      
                                                        =  loop(xs',xs,pp,ss)                   
        

WORST_CASE(?,O(n^2))