WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            even(Cons(x,Nil())) -> False()
            even(Cons(x',Cons(x,xs))) -> even(xs)
            even(Nil()) -> True()
            goal(x,y) -> and(lte(x,y),even(x))
            lte(Cons(x,xs),Nil()) -> False()
            lte(Cons(x',xs'),Cons(x,xs)) -> lte(xs',xs)
            lte(Nil(),y) -> True()
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
        - Signature:
            {and/2,even/1,goal/2,lte/2,notEmpty/1} / {Cons/2,False/0,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,even,goal,lte,notEmpty} and constructors {Cons,False
            ,Nil,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(and) = {1,2}
        
        Following symbols are considered usable:
          {and,even,goal,lte,notEmpty}
        TcT has computed the following interpretation:
              p(Cons) = [1] x2 + [3]          
             p(False) = [0]                   
               p(Nil) = [4]                   
              p(True) = [0]                   
               p(and) = [1] x1 + [1] x2 + [9] 
              p(even) = [4] x1 + [2]          
              p(goal) = [8] x1 + [3] x2 + [15]
               p(lte) = [3] x1 + [2] x2 + [4] 
          p(notEmpty) = [2]                   
        
        Following rules are strictly oriented:
                 even(Cons(x,Nil())) = [30]                   
                                     > [0]                    
                                     = False()                
        
           even(Cons(x',Cons(x,xs))) = [4] xs + [26]          
                                     > [4] xs + [2]           
                                     = even(xs)               
        
                         even(Nil()) = [18]                   
                                     > [0]                    
                                     = True()                 
        
               lte(Cons(x,xs),Nil()) = [3] xs + [21]          
                                     > [0]                    
                                     = False()                
        
        lte(Cons(x',xs'),Cons(x,xs)) = [2] xs + [3] xs' + [19]
                                     > [2] xs + [3] xs' + [4] 
                                     = lte(xs',xs)            
        
                        lte(Nil(),y) = [2] y + [16]           
                                     > [0]                    
                                     = True()                 
        
                notEmpty(Cons(x,xs)) = [2]                    
                                     > [0]                    
                                     = True()                 
        
                     notEmpty(Nil()) = [2]                    
                                     > [0]                    
                                     = False()                
        
        
        Following rules are (at-least) weakly oriented:
        and(False(),False()) =  [9]                  
                             >= [0]                  
                             =  False()              
        
         and(False(),True()) =  [9]                  
                             >= [0]                  
                             =  False()              
        
         and(True(),False()) =  [9]                  
                             >= [0]                  
                             =  False()              
        
          and(True(),True()) =  [9]                  
                             >= [0]                  
                             =  True()               
        
                   goal(x,y) =  [8] x + [3] y + [15] 
                             >= [7] x + [2] y + [15] 
                             =  and(lte(x,y),even(x))
        
* Step 2: NaturalMI WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            goal(x,y) -> and(lte(x,y),even(x))
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
            even(Cons(x,Nil())) -> False()
            even(Cons(x',Cons(x,xs))) -> even(xs)
            even(Nil()) -> True()
            lte(Cons(x,xs),Nil()) -> False()
            lte(Cons(x',xs'),Cons(x,xs)) -> lte(xs',xs)
            lte(Nil(),y) -> True()
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
        - Signature:
            {and/2,even/1,goal/2,lte/2,notEmpty/1} / {Cons/2,False/0,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,even,goal,lte,notEmpty} and constructors {Cons,False
            ,Nil,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(and) = {1,2}
        
        Following symbols are considered usable:
          {and,even,goal,lte,notEmpty}
        TcT has computed the following interpretation:
              p(Cons) = [2]                  
             p(False) = [1]                  
               p(Nil) = [1]                  
              p(True) = [1]                  
               p(and) = [6] x1 + [1] x2 + [4]
              p(even) = [3]                  
              p(goal) = [2] x1 + [15]        
               p(lte) = [1]                  
          p(notEmpty) = [8] x1 + [8]         
        
        Following rules are strictly oriented:
        goal(x,y) = [2] x + [15]         
                  > [13]                 
                  = and(lte(x,y),even(x))
        
        
        Following rules are (at-least) weakly oriented:
                and(False(),False()) =  [11]       
                                     >= [1]        
                                     =  False()    
        
                 and(False(),True()) =  [11]       
                                     >= [1]        
                                     =  False()    
        
                 and(True(),False()) =  [11]       
                                     >= [1]        
                                     =  False()    
        
                  and(True(),True()) =  [11]       
                                     >= [1]        
                                     =  True()     
        
                 even(Cons(x,Nil())) =  [3]        
                                     >= [1]        
                                     =  False()    
        
           even(Cons(x',Cons(x,xs))) =  [3]        
                                     >= [3]        
                                     =  even(xs)   
        
                         even(Nil()) =  [3]        
                                     >= [1]        
                                     =  True()     
        
               lte(Cons(x,xs),Nil()) =  [1]        
                                     >= [1]        
                                     =  False()    
        
        lte(Cons(x',xs'),Cons(x,xs)) =  [1]        
                                     >= [1]        
                                     =  lte(xs',xs)
        
                        lte(Nil(),y) =  [1]        
                                     >= [1]        
                                     =  True()     
        
                notEmpty(Cons(x,xs)) =  [24]       
                                     >= [1]        
                                     =  True()     
        
                     notEmpty(Nil()) =  [16]       
                                     >= [1]        
                                     =  False()    
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            and(False(),False()) -> False()
            and(False(),True()) -> False()
            and(True(),False()) -> False()
            and(True(),True()) -> True()
            even(Cons(x,Nil())) -> False()
            even(Cons(x',Cons(x,xs))) -> even(xs)
            even(Nil()) -> True()
            goal(x,y) -> and(lte(x,y),even(x))
            lte(Cons(x,xs),Nil()) -> False()
            lte(Cons(x',xs'),Cons(x,xs)) -> lte(xs',xs)
            lte(Nil(),y) -> True()
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
        - Signature:
            {and/2,even/1,goal/2,lte/2,notEmpty/1} / {Cons/2,False/0,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,even,goal,lte,notEmpty} and constructors {Cons,False
            ,Nil,True}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))