YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1) = x1 + 4
  f#_A(x1) = x1 + 3
  0_A = 2
  0#_A = 3
  cons_A(x1,x2) = 0
  cons#_A(x1,x2) = 0
  n__f_A(x1) = x1 + 4
  n__f#_A(x1) = 2
  n__s_A(x1) = x1 + 3
  n__s#_A(x1) = 0
  n__0_A = 2
  n__0#_A = 0
  s_A(x1) = x1 + 3
  s#_A(x1) = 4
  p_A(x1) = 2
  p#_A(x1) = 4
  activate_A(x1) = x1 + 1
  activate#_A(x1) = x1 + 1

precedence:

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