Suffix Tree Sliding Window Update Strategy Proof

Hello,
i have read paper "Data Compression with Finite Windows" by Fiala and
Green and PhD. Thesis of N. Jesper Larsson. They both address the
problem of using suffix tree to maintain ZL77-like sliding window. To
keep offsets valid, they use percolating update strategy. They manage
to prove linearity of such approach, but they fail to prove that it
actually keeps those offsets valid. Well, they try, but Larsson's attempt
is obviously incorrect and i have my doubts about Fiala and Green. Is
there any other paper, hopefully with correct proof?

All suggestions welcome,
Martin Senft