YES

TRS:

  f(0()) -> cons(0(),n__f(s(0())))
  f(s(0())) -> f(p(s(0())))
  p(s(X)) -> X
  f(X) -> n__f(X)
  activate(n__f(X)) -> f(X)
  activate(X) -> X

max/plus interpretations on N:

  f_A(x1) = max{18, 1 + x1}
  f#_A(x1) = max{5, 1 + x1}
  0_A = 6
  0#_A = 13
  cons_A(x1,x2) = max{18, 8, 16 + x2}
  cons#_A(x1,x2) = max{6, 6, 6}
  n__f_A(x1) = max{2, -12 + x1}
  n__f#_A(x1) = max{2, 0}
  s_A(x1) = max{4, 5 + x1}
  s#_A(x1) = max{4, 3}
  p_A(x1) = max{1, -5 + x1}
  p#_A(x1) = max{4, 4}
  activate_A(x1) = max{0, 16 + x1}
  activate#_A(x1) = max{0, 14 + x1}

precedence:

  0 = activate > f > cons = n__f = s > p