YES

TRS:

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

max/plus interpretations on N:

  -_A(x1,x2) = max{17, 1 + x1, 19}
  -#_A(x1,x2) = max{8, -5, 9}
  0_A = 0
  0#_A = 0
  s_A(x1) = max{9, 16 + x1}
  s#_A(x1) = max{11, 12}
  p_A(x1) = max{1, -16 + x1}
  p#_A(x1) = max{12, -22 + x1}
  f_A(x1,x2) = max{0, 2, 1}
  f#_A(x1,x2) = max{0, 1 + x1, -4 + x2}

precedence:

  f > - = 0 = s = p