create or replace function repString(s) as (
  if (length(s) < 2, null,
     (with recursive size_t as (select length(s) as size),
      cte as
        (select ((size % 2) + (size // 2)) as len, '' as t, false as found
         from size_t
         union all
         select len-1 as len,
                s[1:len] as t,
                s == (repeat(s[1:len], (size // len))
                     || coalesce(t[1:(size % len)], ''))
                as found
         from cte, size_t
         where len > 0 and found = false
       )
       select first(t)
       from cte
       where found
  ))
);

select s, repString(s)
from unnest(
   [
    '1001110011',
    '1110111011',
    '0010010010',
    '1010101010',
    '1111111111',
    '0100101101',
    '0100100',
    '101',
    '11',
    '00',
    '1'
    ]) _(s);