YES

TRS:

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

linear polynomial interpretations on N:

  g_A(x1) = 2
  g#_A(x1) = x1 + 3
  h_A(x1) = 1
  h#_A(x1) = x1
  f_A(x1,x2) = 0
  f#_A(x1,x2) = 0

precedence:

  g > h = f