Deciding conjugacy in sylvester monoids and other homogeneous monoids
  We give a combinatorial characterization of conjugacy in the sylvester monoid (the monoid of binary search trees), showing that conjugacy is decidable for this monoid. We then prove that conjugacy is undecidable in general for homogeneous monoids and even for multihomogeneous monoids. 
Alan J. Cain, Ant\'onio Malheiro
math.GR