YES

TRS:

  f(f(x)) -> f(g(f(x),x))
  f(f(x)) -> f(h(f(x),f(x)))
  g(x,y) -> y
  h(x,x) -> g(x,0())

max/plus interpretations on N:

  f_A(x1) = max{7, 5 + x1}
  f#_A(x1) = max{3, x1}
  g_A(x1,x2) = max{4, -1, 1 + x2}
  g#_A(x1,x2) = max{2, 6, 6}
  h_A(x1,x2) = max{4, -1, 0}
  h#_A(x1,x2) = max{7, 1, -1}
  0_A = 1
  0#_A = 2

precedence:

  f > h > g = 0