YES

TRS:

  f(0()) -> cons(0(),n__f(n__s(n__0())))
  f(s(0())) -> f(p(s(0())))
  p(s(X)) -> X
  f(X) -> n__f(X)
  s(X) -> n__s(X)
  0() -> n__0()
  activate(n__f(X)) -> f(activate(X))
  activate(n__s(X)) -> s(activate(X))
  activate(n__0()) -> 0()
  activate(X) -> X

max/plus interpretations on N:

  f_A(x1) = max{10, 5 + x1}
  f#_A(x1) = max{3, 9 + x1}
  0_A = 4
  0#_A = 5
  cons_A(x1,x2) = max{10, 10, 1 + x2}
  cons#_A(x1,x2) = max{12, 4, 2}
  n__f_A(x1) = max{9, 5 + x1}
  n__f#_A(x1) = max{7, 9 + x1}
  n__s_A(x1) = max{0, 3 + x1}
  n__s#_A(x1) = max{0, 0}
  n__0_A = 1
  n__0#_A = 4
  s_A(x1) = max{0, 3 + x1}
  s#_A(x1) = max{6, 1}
  p_A(x1) = max{6, -2 + x1}
  p#_A(x1) = max{7, 10}
  activate_A(x1) = max{3, 3 + x1}
  activate#_A(x1) = max{2, 8 + x1}

precedence:

  activate > n__s > s > 0 > f > cons = n__f = n__0 = p