  In this paper we present two algorithms for the following problem: given a
string and a rational $e > 1$, detect in the online fashion the earliest
occurrence of a repetition of exponent $\ge e$ in the string.
  1. The first algorithm supports the backtrack operation removing the last
letter of the input string. This solution runs in $O(n\log m)$ time and $O(m)$
space, where $m$ is the maximal length of a string generated during the
execution of a given sequence of $n$ read and backtrack operations.
  2. The second algorithm works in $O(n\log\sigma)$ time and $O(n)$ space,
where $n$ is the length of the input string and $\sigma$ is the number of
distinct letters. This algorithm is relatively simple and requires much less
memory than the previously known solution with the same working time and space.
a string generated during the execution of a given sequence of $n$ read and
backtrack operations.
