MAYBE
Trs:
 {                  sqr(0()) -> 0(),
                   sqr(s(X)) -> s(n__add(sqr(activate(X)), dbl(activate(X)))),
                    terms(N) -> cons(recip(sqr(N)), n__terms(s(N))),
                    terms(X) -> n__terms(X),
                 add(0(), X) -> X,
                add(s(X), Y) -> s(n__add(activate(X), Y)),
                 add(X1, X2) -> n__add(X1, X2),
                        s(X) -> n__s(X),
                    dbl(0()) -> 0(),
                   dbl(s(X)) -> s(n__s(n__dbl(activate(X)))),
                      dbl(X) -> n__dbl(X),
               first(0(), X) -> nil(),
     first(s(X), cons(Y, Z)) -> cons(Y, n__first(activate(X), activate(Z))),
               first(X1, X2) -> n__first(X1, X2),
       activate(n__terms(X)) -> terms(X),
    activate(n__add(X1, X2)) -> add(X1, X2),
           activate(n__s(X)) -> s(X),
         activate(n__dbl(X)) -> dbl(X),
  activate(n__first(X1, X2)) -> first(X1, X2),
                 activate(X) -> X}
 Comment:
  We consider a duplicating trs.
  FAIL:
   Open