YES

TRS:

  f(0()) -> cons(0())
  f(s(0())) -> f(p(s(0())))
  p(s(X)) -> X

max/plus interpretations on N:

  f_A(x1) = max{0, -2 + x1}
  f#_A(x1) = max{7, x1}
  0_A = 1
  0#_A = 9
  cons_A(x1) = max{0, 0}
  cons#_A(x1) = max{7, 2}
  s_A(x1) = max{9, 7 + x1}
  s#_A(x1) = max{9, 5}
  p_A(x1) = max{4, -5 + x1}
  p#_A(x1) = max{6, 6}

precedence:

  s > f > 0 = cons = p