YES

TRS:

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

linear polynomial interpretations on N:

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

precedence:

  g > f = h