YES

linear polynomial interpretations on natural numbers:

  g_A(x1,x2) = x2
  h_A(x1) = x1
  f_A(x1,x2) = x2
  a_A = 1
  b_A = 0
  F_A(x1,x2) = x2



the condition F(x,g(x,b())) ->> F(y,a()) is unsatisfiable for all substitutions.