YES

TRS:

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

max/plus interpretations on N:

  f_A(x1,x2) = max{0, x1, -1}
  f#_A(x1,x2) = max{2, x1, 2}
  a_A = 3
  a#_A = 0
  g_A(x1) = max{1, -1}
  g#_A(x1) = max{1, 2}
  h_A(x1) = max{4, 1 + x1}
  h#_A(x1) = max{3, -1}

precedence:

  f > g > h > a