YES

TRS:

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

max/plus interpretations on N:

  f_A(x1) = max{0, -2 + x1}
  f#_A(x1) = max{9, 2 + x1}
  0_A = 1
  0#_A = 8
  cons_A(x1) = max{0, 0}
  cons#_A(x1) = max{2, 2}
  s_A(x1) = max{4, 9}
  s#_A(x1) = max{0, 12}
  p_A(x1) = max{3, -1}
  p#_A(x1) = max{10, -2 + x1}

precedence:

  s > f > cons = p > 0