YES
O(n)
TRS:
 {
             sqr(0()) -> 0(),
             sqr(s()) -> s(),
             terms(N) -> cons(recip(sqr(N))),
             dbl(0()) -> 0(),
             dbl(s()) -> s(),
          add(0(), X) -> X,
          add(s(), Y) -> s(),
        first(0(), X) -> nil(),
  first(s(), cons(Y)) -> cons(Y)
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
               sqr(0()) -> 0(),
               sqr(s()) -> s(),
               terms(N) -> cons(recip(sqr(N))),
               dbl(0()) -> 0(),
               dbl(s()) -> s(),
            add(0(), X) -> X,
            add(s(), Y) -> s(),
          first(0(), X) -> nil(),
    first(s(), cons(Y)) -> cons(Y)
   }
  BOUND:
   Automaton:
    {
     first_0(10, 10) -> 10,
             nil_1() -> 10,
             nil_0() -> 10,
       add_0(10, 10) -> 10,
           dbl_0(10) -> 10,
               s_2() -> 11,
               s_1() -> 11 | 10,
               s_0() -> 10,
               0_2() -> 11,
               0_1() -> 11 | 10,
               0_0() -> 10,
         terms_0(10) -> 10,
           sqr_1(10) -> 11,
           sqr_0(10) -> 10,
         recip_1(11) -> 10,
         recip_0(10) -> 10,
          cons_1(10) -> 10,
          cons_0(10) -> 10
    }
   Strict:
    {}
   Qed