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 + 4,
   
   [f](x0, x1) = 2x0 + 4x1 + 1,
   
   [g](x0) = 4x0 + 1
  orientation:
   f(x,g(x)) = 18x + 5 >= x = x
   
   f(x,h(y)) = 2x + 4y + 17 >= 2x + 4y + 9 = f(h(x),y)
  problem:
   
  Qed