YES

Problem:
 active(zeros()) -> mark(cons(0(),zeros()))
 active(tail(cons(X,XS))) -> mark(XS)
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(tail(X)) -> tail(active(X))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 tail(mark(X)) -> mark(tail(X))
 proper(zeros()) -> ok(zeros())
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(0()) -> ok(0())
 proper(tail(X)) -> tail(proper(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 tail(ok(X)) -> ok(tail(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [mark](x0) = x0,
   
   [top](x0) = 2x0,
   
   [active](x0) = x0,
   
   [cons](x0, x1) = 2x0 + x1,
   
   [tail](x0) = 2x0 + 2,
   
   [zeros] = 0,
   
   [ok](x0) = x0,
   
   [proper](x0) = x0,
   
   [0] = 0
  orientation:
   active(zeros()) = 0 >= 0 = mark(cons(0(),zeros()))
   
   active(tail(cons(X,XS))) = 4X + 2XS + 2 >= XS = mark(XS)
   
   active(cons(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = cons(active(X1),X2)
   
   active(tail(X)) = 2X + 2 >= 2X + 2 = tail(active(X))
   
   cons(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(cons(X1,X2))
   
   tail(mark(X)) = 2X + 2 >= 2X + 2 = mark(tail(X))
   
   proper(zeros()) = 0 >= 0 = ok(zeros())
   
   proper(cons(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = cons(proper(X1),proper(X2))
   
   proper(0()) = 0 >= 0 = ok(0())
   
   proper(tail(X)) = 2X + 2 >= 2X + 2 = tail(proper(X))
   
   cons(ok(X1),ok(X2)) = 2X1 + X2 >= 2X1 + X2 = ok(cons(X1,X2))
   
   tail(ok(X)) = 2X + 2 >= 2X + 2 = ok(tail(X))
   
   top(mark(X)) = 2X >= 2X = top(proper(X))
   
   top(ok(X)) = 2X >= 2X = top(active(X))
  problem:
   active(zeros()) -> mark(cons(0(),zeros()))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(tail(X)) -> tail(active(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   tail(mark(X)) -> mark(tail(X))
   proper(zeros()) -> ok(zeros())
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(0()) -> ok(0())
   proper(tail(X)) -> tail(proper(X))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   tail(ok(X)) -> ok(tail(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                 [1 0 0]     [0]
    [mark](x0) = [0 1 0]x0 + [0]
                 [0 0 0]     [1],
    
                [1 1 0]     [0]
    [top](x0) = [0 0 0]x0 + [0]
                [0 0 0]     [1],
    
                   [1 1 0]     [0]
    [active](x0) = [0 0 1]x0 + [0]
                   [0 0 0]     [1],
    
                          [1 0 0]  
    [cons](x0, x1) = x0 + [0 0 0]x1
                          [0 0 0]  ,
    
                   
    [tail](x0) = x0
                   ,
    
              [0]
    [zeros] = [1]
              [0],
    
               [1 0 0]  
    [ok](x0) = [0 1 1]x0
               [0 0 0]  ,
    
                   [1 0 0]  
    [proper](x0) = [0 1 0]x0
                   [0 0 0]  ,
    
          [0]
    [0] = [0]
          [0]
   orientation:
                      [1]    [0]                          
    active(zeros()) = [0] >= [0] = mark(cons(0(),zeros()))
                      [1]    [1]                          
    
                          [1 1 0]     [1 0 0]     [0]    [1 1 0]     [1 0 0]     [0]                      
    active(cons(X1,X2)) = [0 0 1]X1 + [0 0 0]X2 + [0] >= [0 0 1]X1 + [0 0 0]X2 + [0] = cons(active(X1),X2)
                          [0 0 0]     [0 0 0]     [1]    [0 0 0]     [0 0 0]     [1]                      
    
                      [1 1 0]    [0]    [1 1 0]    [0]                  
    active(tail(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = tail(active(X))
                      [0 0 0]    [1]    [0 0 0]    [1]                  
    
                        [1 0 0]     [1 0 0]     [0]    [1 0 0]     [1 0 0]     [0]                    
    cons(mark(X1),X2) = [0 1 0]X1 + [0 0 0]X2 + [0] >= [0 1 0]X1 + [0 0 0]X2 + [0] = mark(cons(X1,X2))
                        [0 0 0]     [0 0 0]     [1]    [0 0 0]     [0 0 0]     [1]                    
    
                    [1 0 0]    [0]    [1 0 0]    [0]                
    tail(mark(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = mark(tail(X))
                    [0 0 0]    [1]    [0 0 0]    [1]                
    
                      [0]    [0]              
    proper(zeros()) = [1] >= [1] = ok(zeros())
                      [0]    [0]              
    
                          [1 0 0]     [1 0 0]      [1 0 0]     [1 0 0]                                
    proper(cons(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = cons(proper(X1),proper(X2))
                          [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                                
    
                  [0]    [0]          
    proper(0()) = [0] >= [0] = ok(0())
                  [0]    [0]          
    
                      [1 0 0]     [1 0 0]                   
    proper(tail(X)) = [0 1 0]X >= [0 1 0]X = tail(proper(X))
                      [0 0 0]     [0 0 0]                   
    
                          [1 0 0]     [1 0 0]      [1 0 0]     [1 0 0]                    
    cons(ok(X1),ok(X2)) = [0 1 1]X1 + [0 0 0]X2 >= [0 1 1]X1 + [0 0 0]X2 = ok(cons(X1,X2))
                          [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                    
    
                  [1 0 0]     [1 0 0]               
    tail(ok(X)) = [0 1 1]X >= [0 1 1]X = ok(tail(X))
                  [0 0 0]     [0 0 0]               
    
                   [1 1 0]    [0]    [1 1 0]    [0]                 
    top(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = top(proper(X))
                   [0 0 0]    [1]    [0 0 0]    [1]                 
    
                 [1 1 1]    [0]    [1 1 1]    [0]                 
    top(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = top(active(X))
                 [0 0 0]    [1]    [0 0 0]    [1]                 
   problem:
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(tail(X)) -> tail(active(X))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    tail(mark(X)) -> mark(tail(X))
    proper(zeros()) -> ok(zeros())
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(0()) -> ok(0())
    proper(tail(X)) -> tail(proper(X))
    cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    tail(ok(X)) -> ok(tail(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [mark](x0) = x0 + 4,
     
     [top](x0) = 4x0 + 5,
     
     [active](x0) = x0,
     
     [cons](x0, x1) = x0 + x1 + 4,
     
     [tail](x0) = 2x0 + 4,
     
     [zeros] = 0,
     
     [ok](x0) = x0,
     
     [proper](x0) = x0,
     
     [0] = 6
    orientation:
     active(cons(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = cons(active(X1),X2)
     
     active(tail(X)) = 2X + 4 >= 2X + 4 = tail(active(X))
     
     cons(mark(X1),X2) = X1 + X2 + 8 >= X1 + X2 + 8 = mark(cons(X1,X2))
     
     tail(mark(X)) = 2X + 12 >= 2X + 8 = mark(tail(X))
     
     proper(zeros()) = 0 >= 0 = ok(zeros())
     
     proper(cons(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = cons(proper(X1),proper(X2))
     
     proper(0()) = 6 >= 6 = ok(0())
     
     proper(tail(X)) = 2X + 4 >= 2X + 4 = tail(proper(X))
     
     cons(ok(X1),ok(X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = ok(cons(X1,X2))
     
     tail(ok(X)) = 2X + 4 >= 2X + 4 = ok(tail(X))
     
     top(mark(X)) = 4X + 21 >= 4X + 5 = top(proper(X))
     
     top(ok(X)) = 4X + 5 >= 4X + 5 = top(active(X))
    problem:
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(tail(X)) -> tail(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     proper(zeros()) -> ok(zeros())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(tail(X)) -> tail(proper(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     tail(ok(X)) -> ok(tail(X))
     top(ok(X)) -> top(active(X))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [mark](x0) = x0 + 2,
      
      [top](x0) = 2x0 + 2,
      
      [active](x0) = x0,
      
      [cons](x0, x1) = x0 + x1,
      
      [tail](x0) = 4x0 + 1,
      
      [zeros] = 2,
      
      [ok](x0) = 2x0 + 1,
      
      [proper](x0) = 3x0,
      
      [0] = 1
     orientation:
      active(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(active(X1),X2)
      
      active(tail(X)) = 4X + 1 >= 4X + 1 = tail(active(X))
      
      cons(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(cons(X1,X2))
      
      proper(zeros()) = 6 >= 5 = ok(zeros())
      
      proper(cons(X1,X2)) = 3X1 + 3X2 >= 3X1 + 3X2 = cons(proper(X1),proper(X2))
      
      proper(0()) = 3 >= 3 = ok(0())
      
      proper(tail(X)) = 12X + 3 >= 12X + 1 = tail(proper(X))
      
      cons(ok(X1),ok(X2)) = 2X1 + 2X2 + 2 >= 2X1 + 2X2 + 1 = ok(cons(X1,X2))
      
      tail(ok(X)) = 8X + 5 >= 8X + 3 = ok(tail(X))
      
      top(ok(X)) = 4X + 4 >= 2X + 2 = top(active(X))
     problem:
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(tail(X)) -> tail(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [mark](x0) = x0,
       
       [active](x0) = x0,
       
       [cons](x0, x1) = 2x0 + x1 + 4,
       
       [tail](x0) = x0 + 6,
       
       [ok](x0) = x0,
       
       [proper](x0) = 4x0,
       
       [0] = 0
      orientation:
       active(cons(X1,X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = cons(active(X1),X2)
       
       active(tail(X)) = X + 6 >= X + 6 = tail(active(X))
       
       cons(mark(X1),X2) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = mark(cons(X1,X2))
       
       proper(cons(X1,X2)) = 8X1 + 4X2 + 16 >= 8X1 + 4X2 + 4 = cons(proper(X1),proper(X2))
       
       proper(0()) = 0 >= 0 = ok(0())
      problem:
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(tail(X)) -> tail(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       proper(0()) -> ok(0())
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [mark](x0) = x0,
        
        [active](x0) = x0,
        
        [cons](x0, x1) = 4x0 + 4x1 + 2,
        
        [tail](x0) = x0,
        
        [ok](x0) = x0 + 1,
        
        [proper](x0) = x0 + 6,
        
        [0] = 2
       orientation:
        active(cons(X1,X2)) = 4X1 + 4X2 + 2 >= 4X1 + 4X2 + 2 = cons(active(X1),X2)
        
        active(tail(X)) = X >= X = tail(active(X))
        
        cons(mark(X1),X2) = 4X1 + 4X2 + 2 >= 4X1 + 4X2 + 2 = mark(cons(X1,X2))
        
        proper(0()) = 8 >= 3 = ok(0())
       problem:
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(tail(X)) -> tail(active(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
       Matrix Interpretation Processor: dim=1
        
        interpretation:
         [mark](x0) = x0 + 4,
         
         [active](x0) = x0,
         
         [cons](x0, x1) = 4x0 + x1,
         
         [tail](x0) = x0 + 2
        orientation:
         active(cons(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = cons(active(X1),X2)
         
         active(tail(X)) = X + 2 >= X + 2 = tail(active(X))
         
         cons(mark(X1),X2) = 4X1 + X2 + 16 >= 4X1 + X2 + 4 = mark(cons(X1,X2))
        problem:
         active(cons(X1,X2)) -> cons(active(X1),X2)
         active(tail(X)) -> tail(active(X))
        Matrix Interpretation Processor: dim=1
         
         interpretation:
          [active](x0) = 2x0,
          
          [cons](x0, x1) = 2x0 + 4x1 + 4,
          
          [tail](x0) = x0
         orientation:
          active(cons(X1,X2)) = 4X1 + 8X2 + 8 >= 4X1 + 4X2 + 4 = cons(active(X1),X2)
          
          active(tail(X)) = 2X >= 2X = tail(active(X))
         problem:
          active(tail(X)) -> tail(active(X))
         Matrix Interpretation Processor: dim=3
          
          interpretation:
                          [1 1 0]  
           [active](x0) = [0 1 0]x0
                          [0 0 0]  ,
           
                        [1 0 0]     [0]
           [tail](x0) = [0 1 0]x0 + [1]
                        [0 0 0]     [0]
          orientation:
                             [1 1 0]    [1]    [1 1 0]    [0]                  
           active(tail(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = tail(active(X))
                             [0 0 0]    [0]    [0 0 0]    [0]                  
          problem:
           
          Qed