YES

TRS:

  f(g(x),g(y)) -> f(p(f(g(x),s(y))),g(s(p(x))))
  p(0()) -> g(0())
  g(s(p(x))) -> p(x)

max/plus interpretations on N:

  f_A(x1,x2) = max{1, -5, -5}
  f#_A(x1,x2) = max{0, 10 + x1, 19}
  g_A(x1) = max{12, -6 + x1}
  g#_A(x1) = max{20, 21}
  p_A(x1) = max{8, -6 + x1}
  p#_A(x1) = max{1, 2 + x1}
  s_A(x1) = max{13, 25 + x1}
  s#_A(x1) = max{21, -1}
  0_A = 19
  0#_A = 22

precedence:

  f > p > g = 0 > s