We present an algorithm for detecting long similar fragments occurring at least twice in a set of biological sequences. The problem becomes computationally challenging when the frequency of a repeat is allowed to increase and when a non-negligible number of insertions, deletions and substitutions are allowed. We introduce in this paper an algorithm, Rime1 (for Repeat Identification: long, Multiple, and with Edits) that performs this task, and manages instances whose size and combination of parameters cannot be handled by other currently existing methods. This is achieved by using a filter as a preprocessing step, and by then exploiting the information gathered by the filter in the following actual repeat inference step. To the best of our knowledge, Rime is the first algorithm that can accurately deal with very long repeats (up to a few thousands), occurring possibly several times, and with a rate of differences (substitutions and indels) allowed among copies of a same repeat of 10-15% or even more.