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