YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1,x2) = x1 + x2 + 2
  f#_A(x1,x2) = x1 + x2 + 2
  a_A = 1
  a#_A = 1
  g_A(x1) = x1 + 1
  g#_A(x1) = x1 + 1

precedence:

  a > f > g