A rational relation is conjugate if every pair of related words are
conjugates. It is shown that checking whether a rational relation is conjugate
is decidable. For this, we generalise the Lyndon-Sch\"utzenberger's theorem
from word combinatorics. A consequence of the generalisation is that a set of
pairs generated by a sumfree rational expression is conjugate if and only if
there is a word witnessing the conjugacy of all the pairs

Aiswarya, C.