  We give an example of two JSJ decompositions of a group that are not related
by conjugation, conjugation of edge-inclusions, and slide moves. This answers
the question of Rips and Sela stated in "Cyclic splittings of finitely
presented groups and the canonical JSJ decomposition," Ann. of Math. 146
(1997), 53-109.
  On the other hand we observe that any two JSJ decompositions of a group are
related by an elementary deformation, and that strongly slide-free JSJ
decompositions are genuinely unique. These results hold for the decompositions
of Rips and Sela, Dunwoody and Sageev, and Fujiwara and Papasoglu, and also for
accessible decompositions.
