YES

TRS:

  g(x,y) -> x
  g(x,y) -> y
  f(s(x),y,y) -> f(y,x,s(x))

max/plus interpretations on N:

  g_A(x1,x2) = max{0, x1, x2}
  g#_A(x1,x2) = max{0, x1, x2}
  f_A(x1,x2,x3) = max{0, x1, -1, x3}
  f#_A(x1,x2,x3) = max{7, 5 + x1, 6 + x2, 1 + x3}
  s_A(x1) = max{4, 3 + x1}
  s#_A(x1) = max{0, -1}

precedence:

  g = s > f