YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1,x2) = x1 + 1
  f#_A(x1,x2) = x2
  g_A(x1,x2) = 1
  g#_A(x1,x2) = 0

precedence:

  f > g