YES

Problem:
 active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
 active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
 active(from(X)) -> mark(cons(X,from(s(X))))
 active(2nd(X)) -> 2nd(active(X))
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(from(X)) -> from(active(X))
 active(s(X)) -> s(active(X))
 active(cons1(X1,X2)) -> cons1(active(X1),X2)
 active(cons1(X1,X2)) -> cons1(X1,active(X2))
 2nd(mark(X)) -> mark(2nd(X))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 from(mark(X)) -> mark(from(X))
 s(mark(X)) -> mark(s(X))
 cons1(mark(X1),X2) -> mark(cons1(X1,X2))
 cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
 proper(2nd(X)) -> 2nd(proper(X))
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(from(X)) -> from(proper(X))
 proper(s(X)) -> s(proper(X))
 proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
 2nd(ok(X)) -> ok(2nd(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 from(ok(X)) -> ok(from(X))
 s(ok(X)) -> ok(s(X))
 cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [top](x0) = 2x0,
   
   [ok](x0) = 4x0 + 1,
   
   [proper](x0) = x0,
   
   [s](x0) = 2x0,
   
   [from](x0) = x0,
   
   [mark](x0) = x0,
   
   [active](x0) = 4x0,
   
   [2nd](x0) = 2x0,
   
   [cons1](x0, x1) = x0 + x1,
   
   [cons](x0, x1) = 2x0 + x1
  orientation:
   active(2nd(cons1(X,cons(Y,Z)))) = 8X + 16Y + 8Z >= Y = mark(Y)
   
   active(2nd(cons(X,X1))) = 16X + 8X1 >= 2X + 2X1 = mark(2nd(cons1(X,X1)))
   
   active(from(X)) = 4X >= 4X = mark(cons(X,from(s(X))))
   
   active(2nd(X)) = 8X >= 8X = 2nd(active(X))
   
   active(cons(X1,X2)) = 8X1 + 4X2 >= 8X1 + X2 = cons(active(X1),X2)
   
   active(from(X)) = 4X >= 4X = from(active(X))
   
   active(s(X)) = 8X >= 8X = s(active(X))
   
   active(cons1(X1,X2)) = 4X1 + 4X2 >= 4X1 + X2 = cons1(active(X1),X2)
   
   active(cons1(X1,X2)) = 4X1 + 4X2 >= X1 + 4X2 = cons1(X1,active(X2))
   
   2nd(mark(X)) = 2X >= 2X = mark(2nd(X))
   
   cons(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(cons(X1,X2))
   
   from(mark(X)) = X >= X = mark(from(X))
   
   s(mark(X)) = 2X >= 2X = mark(s(X))
   
   cons1(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(cons1(X1,X2))
   
   cons1(X1,mark(X2)) = X1 + X2 >= X1 + X2 = mark(cons1(X1,X2))
   
   proper(2nd(X)) = 2X >= 2X = 2nd(proper(X))
   
   proper(cons(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = cons(proper(X1),proper(X2))
   
   proper(from(X)) = X >= X = from(proper(X))
   
   proper(s(X)) = 2X >= 2X = s(proper(X))
   
   proper(cons1(X1,X2)) = X1 + X2 >= X1 + X2 = cons1(proper(X1),proper(X2))
   
   2nd(ok(X)) = 8X + 2 >= 8X + 1 = ok(2nd(X))
   
   cons(ok(X1),ok(X2)) = 8X1 + 4X2 + 3 >= 8X1 + 4X2 + 1 = ok(cons(X1,X2))
   
   from(ok(X)) = 4X + 1 >= 4X + 1 = ok(from(X))
   
   s(ok(X)) = 8X + 2 >= 8X + 1 = ok(s(X))
   
   cons1(ok(X1),ok(X2)) = 4X1 + 4X2 + 2 >= 4X1 + 4X2 + 1 = ok(cons1(X1,X2))
   
   top(mark(X)) = 2X >= 2X = top(proper(X))
   
   top(ok(X)) = 8X + 2 >= 8X = top(active(X))
  problem:
   active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
   active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
   active(from(X)) -> mark(cons(X,from(s(X))))
   active(2nd(X)) -> 2nd(active(X))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(from(X)) -> from(active(X))
   active(s(X)) -> s(active(X))
   active(cons1(X1,X2)) -> cons1(active(X1),X2)
   active(cons1(X1,X2)) -> cons1(X1,active(X2))
   2nd(mark(X)) -> mark(2nd(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   from(mark(X)) -> mark(from(X))
   s(mark(X)) -> mark(s(X))
   cons1(mark(X1),X2) -> mark(cons1(X1,X2))
   cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
   proper(2nd(X)) -> 2nd(proper(X))
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(from(X)) -> from(proper(X))
   proper(s(X)) -> s(proper(X))
   proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
   from(ok(X)) -> ok(from(X))
   top(mark(X)) -> top(proper(X))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [top](x0) = 2x0 + 6,
    
    [ok](x0) = 4x0,
    
    [proper](x0) = x0,
    
    [s](x0) = x0,
    
    [from](x0) = x0,
    
    [mark](x0) = x0 + 2,
    
    [active](x0) = 2x0 + 2,
    
    [2nd](x0) = 2x0 + 6,
    
    [cons1](x0, x1) = x0 + x1,
    
    [cons](x0, x1) = x0 + x1
   orientation:
    active(2nd(cons1(X,cons(Y,Z)))) = 4X + 4Y + 4Z + 14 >= Y + 2 = mark(Y)
    
    active(2nd(cons(X,X1))) = 4X + 4X1 + 14 >= 2X + 2X1 + 8 = mark(2nd(cons1(X,X1)))
    
    active(from(X)) = 2X + 2 >= 2X + 2 = mark(cons(X,from(s(X))))
    
    active(2nd(X)) = 4X + 14 >= 4X + 10 = 2nd(active(X))
    
    active(cons(X1,X2)) = 2X1 + 2X2 + 2 >= 2X1 + X2 + 2 = cons(active(X1),X2)
    
    active(from(X)) = 2X + 2 >= 2X + 2 = from(active(X))
    
    active(s(X)) = 2X + 2 >= 2X + 2 = s(active(X))
    
    active(cons1(X1,X2)) = 2X1 + 2X2 + 2 >= 2X1 + X2 + 2 = cons1(active(X1),X2)
    
    active(cons1(X1,X2)) = 2X1 + 2X2 + 2 >= X1 + 2X2 + 2 = cons1(X1,active(X2))
    
    2nd(mark(X)) = 2X + 10 >= 2X + 8 = mark(2nd(X))
    
    cons(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(cons(X1,X2))
    
    from(mark(X)) = X + 2 >= X + 2 = mark(from(X))
    
    s(mark(X)) = X + 2 >= X + 2 = mark(s(X))
    
    cons1(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(cons1(X1,X2))
    
    cons1(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = mark(cons1(X1,X2))
    
    proper(2nd(X)) = 2X + 6 >= 2X + 6 = 2nd(proper(X))
    
    proper(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(proper(X1),proper(X2))
    
    proper(from(X)) = X >= X = from(proper(X))
    
    proper(s(X)) = X >= X = s(proper(X))
    
    proper(cons1(X1,X2)) = X1 + X2 >= X1 + X2 = cons1(proper(X1),proper(X2))
    
    from(ok(X)) = 4X >= 4X = ok(from(X))
    
    top(mark(X)) = 2X + 10 >= 2X + 6 = top(proper(X))
   problem:
    active(from(X)) -> mark(cons(X,from(s(X))))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(from(X)) -> from(active(X))
    active(s(X)) -> s(active(X))
    active(cons1(X1,X2)) -> cons1(active(X1),X2)
    active(cons1(X1,X2)) -> cons1(X1,active(X2))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    from(mark(X)) -> mark(from(X))
    s(mark(X)) -> mark(s(X))
    cons1(mark(X1),X2) -> mark(cons1(X1,X2))
    cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
    proper(2nd(X)) -> 2nd(proper(X))
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(from(X)) -> from(proper(X))
    proper(s(X)) -> s(proper(X))
    proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
    from(ok(X)) -> ok(from(X))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [ok](x0) = 3x0,
     
     [proper](x0) = x0,
     
     [s](x0) = 2x0,
     
     [from](x0) = 2x0,
     
     [mark](x0) = x0,
     
     [active](x0) = 5x0,
     
     [2nd](x0) = x0,
     
     [cons1](x0, x1) = 4x0 + 4x1 + 1,
     
     [cons](x0, x1) = 2x0 + 2x1
    orientation:
     active(from(X)) = 10X >= 10X = mark(cons(X,from(s(X))))
     
     active(cons(X1,X2)) = 10X1 + 10X2 >= 10X1 + 2X2 = cons(active(X1),X2)
     
     active(from(X)) = 10X >= 10X = from(active(X))
     
     active(s(X)) = 10X >= 10X = s(active(X))
     
     active(cons1(X1,X2)) = 20X1 + 20X2 + 5 >= 20X1 + 4X2 + 1 = cons1(active(X1),X2)
     
     active(cons1(X1,X2)) = 20X1 + 20X2 + 5 >= 4X1 + 20X2 + 1 = cons1(X1,active(X2))
     
     cons(mark(X1),X2) = 2X1 + 2X2 >= 2X1 + 2X2 = mark(cons(X1,X2))
     
     from(mark(X)) = 2X >= 2X = mark(from(X))
     
     s(mark(X)) = 2X >= 2X = mark(s(X))
     
     cons1(mark(X1),X2) = 4X1 + 4X2 + 1 >= 4X1 + 4X2 + 1 = mark(cons1(X1,X2))
     
     cons1(X1,mark(X2)) = 4X1 + 4X2 + 1 >= 4X1 + 4X2 + 1 = mark(cons1(X1,X2))
     
     proper(2nd(X)) = X >= X = 2nd(proper(X))
     
     proper(cons(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = cons(proper(X1),proper(X2))
     
     proper(from(X)) = 2X >= 2X = from(proper(X))
     
     proper(s(X)) = 2X >= 2X = s(proper(X))
     
     proper(cons1(X1,X2)) = 4X1 + 4X2 + 1 >= 4X1 + 4X2 + 1 = cons1(proper(X1),proper(X2))
     
     from(ok(X)) = 6X >= 6X = ok(from(X))
    problem:
     active(from(X)) -> mark(cons(X,from(s(X))))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(from(X)) -> from(active(X))
     active(s(X)) -> s(active(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     from(mark(X)) -> mark(from(X))
     s(mark(X)) -> mark(s(X))
     cons1(mark(X1),X2) -> mark(cons1(X1,X2))
     cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
     proper(2nd(X)) -> 2nd(proper(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(from(X)) -> from(proper(X))
     proper(s(X)) -> s(proper(X))
     proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
     from(ok(X)) -> ok(from(X))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [ok](x0) = 4x0,
      
      [proper](x0) = 5x0,
      
      [s](x0) = x0,
      
      [from](x0) = x0,
      
      [mark](x0) = x0,
      
      [active](x0) = 5x0 + 4,
      
      [2nd](x0) = x0,
      
      [cons1](x0, x1) = 4x0 + x1 + 4,
      
      [cons](x0, x1) = 2x0 + 2x1 + 4
     orientation:
      active(from(X)) = 5X + 4 >= 4X + 4 = mark(cons(X,from(s(X))))
      
      active(cons(X1,X2)) = 10X1 + 10X2 + 24 >= 10X1 + 2X2 + 12 = cons(active(X1),X2)
      
      active(from(X)) = 5X + 4 >= 5X + 4 = from(active(X))
      
      active(s(X)) = 5X + 4 >= 5X + 4 = s(active(X))
      
      cons(mark(X1),X2) = 2X1 + 2X2 + 4 >= 2X1 + 2X2 + 4 = mark(cons(X1,X2))
      
      from(mark(X)) = X >= X = mark(from(X))
      
      s(mark(X)) = X >= X = mark(s(X))
      
      cons1(mark(X1),X2) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = mark(cons1(X1,X2))
      
      cons1(X1,mark(X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = mark(cons1(X1,X2))
      
      proper(2nd(X)) = 5X >= 5X = 2nd(proper(X))
      
      proper(cons(X1,X2)) = 10X1 + 10X2 + 20 >= 10X1 + 10X2 + 4 = cons(proper(X1),proper(X2))
      
      proper(from(X)) = 5X >= 5X = from(proper(X))
      
      proper(s(X)) = 5X >= 5X = s(proper(X))
      
      proper(cons1(X1,X2)) = 20X1 + 5X2 + 20 >= 20X1 + 5X2 + 4 = cons1(proper(X1),proper(X2))
      
      from(ok(X)) = 4X >= 4X = ok(from(X))
     problem:
      active(from(X)) -> mark(cons(X,from(s(X))))
      active(from(X)) -> from(active(X))
      active(s(X)) -> s(active(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      from(mark(X)) -> mark(from(X))
      s(mark(X)) -> mark(s(X))
      cons1(mark(X1),X2) -> mark(cons1(X1,X2))
      cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
      proper(2nd(X)) -> 2nd(proper(X))
      proper(from(X)) -> from(proper(X))
      proper(s(X)) -> s(proper(X))
      from(ok(X)) -> ok(from(X))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [ok](x0) = x0,
       
       [proper](x0) = 6x0,
       
       [s](x0) = x0,
       
       [from](x0) = 4x0 + 2,
       
       [mark](x0) = x0,
       
       [active](x0) = 3x0 + 1,
       
       [2nd](x0) = x0 + 2,
       
       [cons1](x0, x1) = x0 + x1,
       
       [cons](x0, x1) = 2x0 + x1 + 5
      orientation:
       active(from(X)) = 12X + 7 >= 6X + 7 = mark(cons(X,from(s(X))))
       
       active(from(X)) = 12X + 7 >= 12X + 6 = from(active(X))
       
       active(s(X)) = 3X + 1 >= 3X + 1 = s(active(X))
       
       cons(mark(X1),X2) = 2X1 + X2 + 5 >= 2X1 + X2 + 5 = mark(cons(X1,X2))
       
       from(mark(X)) = 4X + 2 >= 4X + 2 = mark(from(X))
       
       s(mark(X)) = X >= X = mark(s(X))
       
       cons1(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(cons1(X1,X2))
       
       cons1(X1,mark(X2)) = X1 + X2 >= X1 + X2 = mark(cons1(X1,X2))
       
       proper(2nd(X)) = 6X + 12 >= 6X + 2 = 2nd(proper(X))
       
       proper(from(X)) = 24X + 12 >= 24X + 2 = from(proper(X))
       
       proper(s(X)) = 6X >= 6X = s(proper(X))
       
       from(ok(X)) = 4X + 2 >= 4X + 2 = ok(from(X))
      problem:
       active(from(X)) -> mark(cons(X,from(s(X))))
       active(s(X)) -> s(active(X))
       cons(mark(X1),X2) -> mark(cons(X1,X2))
       from(mark(X)) -> mark(from(X))
       s(mark(X)) -> mark(s(X))
       cons1(mark(X1),X2) -> mark(cons1(X1,X2))
       cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
       proper(s(X)) -> s(proper(X))
       from(ok(X)) -> ok(from(X))
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [ok](x0) = 2x0 + 4,
        
        [proper](x0) = 2x0,
        
        [s](x0) = 2x0,
        
        [from](x0) = 2x0 + 4,
        
        [mark](x0) = x0 + 4,
        
        [active](x0) = 6x0,
        
        [cons1](x0, x1) = x0 + 2x1,
        
        [cons](x0, x1) = x0 + x1
       orientation:
        active(from(X)) = 12X + 24 >= 5X + 8 = mark(cons(X,from(s(X))))
        
        active(s(X)) = 12X >= 12X = s(active(X))
        
        cons(mark(X1),X2) = X1 + X2 + 4 >= X1 + X2 + 4 = mark(cons(X1,X2))
        
        from(mark(X)) = 2X + 12 >= 2X + 8 = mark(from(X))
        
        s(mark(X)) = 2X + 8 >= 2X + 4 = mark(s(X))
        
        cons1(mark(X1),X2) = X1 + 2X2 + 4 >= X1 + 2X2 + 4 = mark(cons1(X1,X2))
        
        cons1(X1,mark(X2)) = X1 + 2X2 + 8 >= X1 + 2X2 + 4 = mark(cons1(X1,X2))
        
        proper(s(X)) = 4X >= 4X = s(proper(X))
        
        from(ok(X)) = 4X + 12 >= 4X + 12 = ok(from(X))
       problem:
        active(s(X)) -> s(active(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        cons1(mark(X1),X2) -> mark(cons1(X1,X2))
        proper(s(X)) -> s(proper(X))
        from(ok(X)) -> ok(from(X))
       Matrix Interpretation Processor: dim=1
        
        interpretation:
         [ok](x0) = 6x0 + 4,
         
         [proper](x0) = 3x0 + 2,
         
         [s](x0) = 3x0 + 2,
         
         [from](x0) = 5x0 + 3,
         
         [mark](x0) = x0 + 1,
         
         [active](x0) = 6x0 + 5,
         
         [cons1](x0, x1) = x0 + x1 + 4,
         
         [cons](x0, x1) = x0 + 2x1 + 1
        orientation:
         active(s(X)) = 18X + 17 >= 18X + 17 = s(active(X))
         
         cons(mark(X1),X2) = X1 + 2X2 + 2 >= X1 + 2X2 + 2 = mark(cons(X1,X2))
         
         cons1(mark(X1),X2) = X1 + X2 + 5 >= X1 + X2 + 5 = mark(cons1(X1,X2))
         
         proper(s(X)) = 9X + 8 >= 9X + 8 = s(proper(X))
         
         from(ok(X)) = 30X + 23 >= 30X + 22 = ok(from(X))
        problem:
         active(s(X)) -> s(active(X))
         cons(mark(X1),X2) -> mark(cons(X1,X2))
         cons1(mark(X1),X2) -> mark(cons1(X1,X2))
         proper(s(X)) -> s(proper(X))
        Matrix Interpretation Processor: dim=1
         
         interpretation:
          [proper](x0) = x0 + 1,
          
          [s](x0) = x0 + 3,
          
          [mark](x0) = x0 + 5,
          
          [active](x0) = x0,
          
          [cons1](x0, x1) = 5x0 + 4x1,
          
          [cons](x0, x1) = x0 + x1
         orientation:
          active(s(X)) = X + 3 >= X + 3 = s(active(X))
          
          cons(mark(X1),X2) = X1 + X2 + 5 >= X1 + X2 + 5 = mark(cons(X1,X2))
          
          cons1(mark(X1),X2) = 5X1 + 4X2 + 25 >= 5X1 + 4X2 + 5 = mark(cons1(X1,X2))
          
          proper(s(X)) = X + 4 >= X + 4 = s(proper(X))
         problem:
          active(s(X)) -> s(active(X))
          cons(mark(X1),X2) -> mark(cons(X1,X2))
          proper(s(X)) -> s(proper(X))
         Matrix Interpretation Processor: dim=3
          
          interpretation:
                          [1 0 0]  
           [proper](x0) = [1 1 0]x0
                          [0 0 0]  ,
           
                     [1 0 0]     [0]
           [s](x0) = [0 1 0]x0 + [1]
                     [0 0 0]     [0],
           
                             [0]
           [mark](x0) = x0 + [1]
                             [1],
           
                          [1 1 0]  
           [active](x0) = [0 1 0]x0
                          [0 1 0]  ,
           
                            [1 0 1]     [1 0 0]  
           [cons](x0, x1) = [0 1 0]x0 + [0 1 0]x1
                            [0 1 0]     [0 0 0]  
          orientation:
                          [1 1 0]    [1]    [1 1 0]    [0]               
           active(s(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = s(active(X))
                          [0 1 0]    [1]    [0 0 0]    [0]               
           
                               [1 0 1]     [1 0 0]     [1]    [1 0 1]     [1 0 0]     [0]                    
           cons(mark(X1),X2) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = mark(cons(X1,X2))
                               [0 1 0]     [0 0 0]     [1]    [0 1 0]     [0 0 0]     [1]                    
           
                          [1 0 0]    [0]    [1 0 0]    [0]               
           proper(s(X)) = [1 1 0]X + [1] >= [1 1 0]X + [1] = s(proper(X))
                          [0 0 0]    [0]    [0 0 0]    [0]               
          problem:
           proper(s(X)) -> s(proper(X))
          Matrix Interpretation Processor: dim=3
           
           interpretation:
                           [1 0 1]  
            [proper](x0) = [0 0 0]x0
                           [0 0 1]  ,
            
                      [1 0 0]     [0]
            [s](x0) = [0 0 0]x0 + [0]
                      [0 0 1]     [1]
           orientation:
                           [1 0 1]    [1]    [1 0 1]    [0]               
            proper(s(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = s(proper(X))
                           [0 0 1]    [1]    [0 0 1]    [1]               
           problem:
            
           Qed