YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0, x1) = 4x0 + x1,
   
   [f](x0) = x0 + 2,
   
   [h](x0, x1) = 4x0 + x1 + 6
  orientation:
   g(f(x),y) = 4x + y + 8 >= 4x + y + 8 = f(h(x,y))
   
   h(x,y) = 4x + y + 6 >= 4x + y + 2 = g(x,f(y))
  problem:
   g(f(x),y) -> f(h(x,y))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [g](x0, x1) = 3x0 + 4x1 + 1,
    
    [f](x0) = 2x0 + 6,
    
    [h](x0, x1) = 3x0 + 2x1 + 6
   orientation:
    g(f(x),y) = 6x + 4y + 19 >= 6x + 4y + 18 = f(h(x,y))
   problem:
    
   Qed