  This paper provides an upper bound for several subsets of maximal repeats and
maximal pairs in compressed strings and also presents a formerly unknown
relationship between maximal pairs and the run-length Burrows-Wheeler
transform.
  This relationship is used to obtain a different proof for the Burrows-Wheeler
conjecture which has recently been proven by Kempa and Kociumaka in "Resolution
of the Burrows-Wheeler Transform Conjecture".
  More formally, this paper proves that a string $S$ with $z$ LZ77-factors and
without $q$-th powers has at most $73(\log_2 |S|)(z+2)^2$ runs in the
run-length Burrows-Wheeler transform and the number of arcs in the compacted
directed acyclic word graph of $S$ is bounded from above by $18q(1+\log_q
|S|)(z+2)^2$.
