YES
O(n^2)
TRS:
 {
         norm(nil()) -> 0(),
       norm(g(x, y)) -> s(norm(x)),
         f(x, nil()) -> g(nil(), x),
       f(x, g(y, z)) -> g(f(x, y), z),
       rem(nil(), y) -> nil(),
   rem(g(x, y), 0()) -> g(x, y),
  rem(g(x, y), s(z)) -> rem(x, z)
 }
 Natural interpretation:
  Strict:
   {
           norm(nil()) -> 0(),
         norm(g(x, y)) -> s(norm(x)),
           f(x, nil()) -> g(nil(), x),
         f(x, g(y, z)) -> g(f(x, y), z),
         rem(nil(), y) -> nil(),
     rem(g(x, y), 0()) -> g(x, y),
    rem(g(x, y), s(z)) -> rem(x, z)
   }
  Weak:
   {}
  Interpretation class: deltarestricted
  [rem](delta, X1, X0) = + 1*X0 + 1*X1 + 0 + 1*X0*delta + 0*X1*delta + 1*delta
  [f](delta, X1, X0) = + 1*X0 + 0*X1 + 1 + 1*X0*delta + 1*X1*delta + 1*delta
  [g](delta, X1, X0) = + 0*X0 + 1*X1 + 1 + 1*X0*delta + 0*X1*delta + 0*delta
  [s](delta, X0) = + 1*X0 + 1 + 0*X0*delta + 0*delta
  [nil](delta) = + 0 + 0*delta
  [norm](delta, X0) = + 1*X0 + 0 + 1*X0*delta + 1*delta
  [0](delta) = + 0 + 0*delta
  rem_tau_1(delta) = delta/(1 + 0 * delta)rem_tau_2(delta) = delta/(1 + 1 * delta)
  f_tau_1(delta) = delta/(0 + 1 * delta)f_tau_2(delta) = delta/(1 + 1 * delta)
  g_tau_1(delta) = delta/(1 + 0 * delta)g_tau_2(delta) = delta/(0 + 1 * delta)
  s_tau_1(delta) = delta/(1 + 0 * delta)
  
  norm_tau_1(delta) = delta/(1 + 1 * delta)
  
  
  Qed