YES

Problem:
 f(x,g(x)) -> x
 f(x,h(y)) -> f(h(x),y)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [h](x0) = x0,
   
   [f](x0, x1) = x0 + x1 + 4,
   
   [g](x0) = 6x0
  orientation:
   f(x,g(x)) = 7x + 4 >= x = x
   
   f(x,h(y)) = x + y + 4 >= x + y + 4 = f(h(x),y)
  problem:
   f(x,h(y)) -> f(h(x),y)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]     [0]
    [h](x0) = [0 0 0]x0 + [0]
              [0 0 1]     [1],
    
                  [1 0 0]     [1 0 1]  
    [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                  [0 0 0]     [0 0 0]  
   orientation:
                [1 0 0]    [1 0 1]    [1]    [1 0 0]    [1 0 1]             
    f(x,h(y)) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = f(h(x),y)
                [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]             
   problem:
    
   Qed