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())

linear polynomial interpretations on N:

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

precedence:

  f > h > g = 0