YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = x0 + 3,
   
   [a] = 0,
   
   [f](x0, x1) = 4x0 + 7x1 + 4
  orientation:
   f(x,x) = 11x + 4 >= 0 = a()
   
   f(g(x),y) = 4x + 7y + 16 >= 4x + 7y + 4 = f(x,y)
  problem:
   
  Qed