YES

TRS:

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

linear polynomial interpretations on N:

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

precedence:

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