WORST_CASE(?,O(n^1))
* Step 1: NaturalMI 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:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        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) = [0]                  
                     p(<) = [0]                  
                  p(Cons) = [1] x1 + [1] x2 + [3]
                 p(False) = [0]                  
                   p(Nil) = [0]                  
                     p(S) = [1] x1 + [0]         
                  p(True) = [0]                  
                  p(goal) = [8]                  
              p(notEmpty) = [6] x1 + [9]         
               p(ordered) = [0]                  
          p(ordered[Ite]) = [8] x1 + [0]         
        
        Following rules are strictly oriented:
                    goal(xs) = [8]                  
                             > [0]                  
                             = ordered(xs)          
        
        notEmpty(Cons(x,xs)) = [6] x + [6] xs + [27]
                             > [0]                  
                             = True()               
        
             notEmpty(Nil()) = [9]                  
                             > [0]                  
                             = False()              
        
        
        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(Cons(x,Nil())) =  [0]                                      
                                        >= [0]                                      
                                        =  True()                                   
        
           ordered(Cons(x',Cons(x,xs))) =  [0]                                      
                                        >= [0]                                      
                                        =  ordered[Ite](<(x',x),Cons(x',Cons(x,xs)))
        
                         ordered(Nil()) =  [0]                                      
                                        >= [0]                                      
                                        =  True()                                   
        
               ordered[Ite](False(),xs) =  [0]                                      
                                        >= [0]                                      
                                        =  False()                                  
        
        ordered[Ite](True(),Cons(x,xs)) =  [0]                                      
                                        >= [0]                                      
                                        =  ordered(xs)                              
        
* Step 2: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            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)
            goal(xs) -> ordered(xs)
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            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:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        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) = [0]         
                     p(<) = [0]         
                  p(Cons) = [1] x1 + [0]
                 p(False) = [0]         
                   p(Nil) = [0]         
                     p(S) = [0]         
                  p(True) = [0]         
                  p(goal) = [8] x1 + [6]
              p(notEmpty) = [8]         
               p(ordered) = [4]         
          p(ordered[Ite]) = [1] x1 + [4]
        
        Following rules are strictly oriented:
        ordered(Cons(x,Nil())) = [4]   
                               > [0]   
                               = True()
        
                ordered(Nil()) = [4]   
                               > [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)                                   
        
                               goal(xs) =  [8] xs + [6]                             
                                        >= [4]                                      
                                        =  ordered(xs)                              
        
                   notEmpty(Cons(x,xs)) =  [8]                                      
                                        >= [0]                                      
                                        =  True()                                   
        
                        notEmpty(Nil()) =  [8]                                      
                                        >= [0]                                      
                                        =  False()                                  
        
           ordered(Cons(x',Cons(x,xs))) =  [4]                                      
                                        >= [4]                                      
                                        =  ordered[Ite](<(x',x),Cons(x',Cons(x,xs)))
        
               ordered[Ite](False(),xs) =  [4]                                      
                                        >= [0]                                      
                                        =  False()                                  
        
        ordered[Ite](True(),Cons(x,xs)) =  [4]                                      
                                        >= [4]                                      
                                        =  ordered(xs)                              
        
* Step 3: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            ordered(Cons(x',Cons(x,xs))) -> ordered[Ite](<(x',x),Cons(x',Cons(x,xs)))
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            goal(xs) -> ordered(xs)
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            ordered(Cons(x,Nil())) -> True()
            ordered(Nil()) -> True()
            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:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        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) = [4]                  
                     p(<) = [0]                  
                  p(Cons) = [1] x2 + [2]         
                 p(False) = [0]                  
                   p(Nil) = [2]                  
                     p(S) = [0]                  
                  p(True) = [0]                  
                  p(goal) = [4] x1 + [11]        
              p(notEmpty) = [2] x1 + [2]         
               p(ordered) = [4] x1 + [8]         
          p(ordered[Ite]) = [8] x1 + [4] x2 + [0]
        
        Following rules are strictly oriented:
        ordered(Cons(x',Cons(x,xs))) = [4] xs + [24]                            
                                     > [4] xs + [16]                            
                                     = ordered[Ite](<(x',x),Cons(x',Cons(x,xs)))
        
        
        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)       
        
                               goal(xs) =  [4] xs + [11]
                                        >= [4] xs + [8] 
                                        =  ordered(xs)  
        
                   notEmpty(Cons(x,xs)) =  [2] xs + [6] 
                                        >= [0]          
                                        =  True()       
        
                        notEmpty(Nil()) =  [6]          
                                        >= [0]          
                                        =  False()      
        
                 ordered(Cons(x,Nil())) =  [24]         
                                        >= [0]          
                                        =  True()       
        
                         ordered(Nil()) =  [16]         
                                        >= [0]          
                                        =  True()       
        
               ordered[Ite](False(),xs) =  [4] xs + [0] 
                                        >= [0]          
                                        =  False()      
        
        ordered[Ite](True(),Cons(x,xs)) =  [4] xs + [8] 
                                        >= [4] xs + [8] 
                                        =  ordered(xs)  
        
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            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()
            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:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))