YES

Problem:
 top(sent(x)) -> top(check(rest(x)))
 rest(nil()) -> sent(nil())
 rest(cons(x,y)) -> sent(y)
 check(sent(x)) -> sent(check(x))
 check(rest(x)) -> rest(check(x))
 check(cons(x,y)) -> cons(check(x),y)
 check(cons(x,y)) -> cons(x,check(y))
 check(cons(x,y)) -> cons(x,y)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [cons](x0, x1) = x0 + 2x1 + 7,
   
   [nil] = 0,
   
   [check](x0) = x0,
   
   [rest](x0) = 2x0,
   
   [top](x0) = 4x0 + 1,
   
   [sent](x0) = 3x0
  orientation:
   top(sent(x)) = 12x + 1 >= 8x + 1 = top(check(rest(x)))
   
   rest(nil()) = 0 >= 0 = sent(nil())
   
   rest(cons(x,y)) = 2x + 4y + 14 >= 3y = sent(y)
   
   check(sent(x)) = 3x >= 3x = sent(check(x))
   
   check(rest(x)) = 2x >= 2x = rest(check(x))
   
   check(cons(x,y)) = x + 2y + 7 >= x + 2y + 7 = cons(check(x),y)
   
   check(cons(x,y)) = x + 2y + 7 >= x + 2y + 7 = cons(x,check(y))
   
   check(cons(x,y)) = x + 2y + 7 >= x + 2y + 7 = cons(x,y)
  problem:
   top(sent(x)) -> top(check(rest(x)))
   rest(nil()) -> sent(nil())
   check(sent(x)) -> sent(check(x))
   check(rest(x)) -> rest(check(x))
   check(cons(x,y)) -> cons(check(x),y)
   check(cons(x,y)) -> cons(x,check(y))
   check(cons(x,y)) -> cons(x,y)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [cons](x0, x1) = 3x0 + 2x1 + 4,
    
    [nil] = 0,
    
    [check](x0) = 3x0,
    
    [rest](x0) = 2x0,
    
    [top](x0) = 4x0,
    
    [sent](x0) = 6x0
   orientation:
    top(sent(x)) = 24x >= 24x = top(check(rest(x)))
    
    rest(nil()) = 0 >= 0 = sent(nil())
    
    check(sent(x)) = 18x >= 18x = sent(check(x))
    
    check(rest(x)) = 6x >= 6x = rest(check(x))
    
    check(cons(x,y)) = 9x + 6y + 12 >= 9x + 2y + 4 = cons(check(x),y)
    
    check(cons(x,y)) = 9x + 6y + 12 >= 3x + 6y + 4 = cons(x,check(y))
    
    check(cons(x,y)) = 9x + 6y + 12 >= 3x + 2y + 4 = cons(x,y)
   problem:
    top(sent(x)) -> top(check(rest(x)))
    rest(nil()) -> sent(nil())
    check(sent(x)) -> sent(check(x))
    check(rest(x)) -> rest(check(x))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
             [0]
     [nil] = [0]
             [1],
     
                   [1 1 0]  
     [check](x0) = [0 0 0]x0
                   [0 0 0]  ,
     
                  [1 0 1]  
     [rest](x0) = [0 1 0]x0
                  [0 0 1]  ,
     
                 [1 0 1]     [1]
     [top](x0) = [1 0 1]x0 + [1]
                 [1 0 1]     [0],
     
                  [1 0 0]  
     [sent](x0) = [0 1 0]x0
                  [0 1 1]  
    orientation:
                    [1 1 1]    [1]    [1 1 1]    [1]                      
     top(sent(x)) = [1 1 1]x + [1] >= [1 1 1]x + [1] = top(check(rest(x)))
                    [1 1 1]    [0]    [1 1 1]    [0]                      
     
                   [1]    [0]              
     rest(nil()) = [0] >= [0] = sent(nil())
                   [1]    [1]              
     
                      [1 1 0]     [1 1 0]                  
     check(sent(x)) = [0 0 0]x >= [0 0 0]x = sent(check(x))
                      [0 0 0]     [0 0 0]                  
     
                      [1 1 1]     [1 1 0]                  
     check(rest(x)) = [0 0 0]x >= [0 0 0]x = rest(check(x))
                      [0 0 0]     [0 0 0]                  
    problem:
     top(sent(x)) -> top(check(rest(x)))
     check(sent(x)) -> sent(check(x))
     check(rest(x)) -> rest(check(x))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [check](x0) = 4x0,
      
      [rest](x0) = x0 + 1,
      
      [top](x0) = x0,
      
      [sent](x0) = 5x0 + 6
     orientation:
      top(sent(x)) = 5x + 6 >= 4x + 4 = top(check(rest(x)))
      
      check(sent(x)) = 20x + 24 >= 20x + 6 = sent(check(x))
      
      check(rest(x)) = 4x + 4 >= 4x + 1 = rest(check(x))
     problem:
      
     Qed