  The well known open \v{C}ern\'y conjecture states that each \san with $n$
states has a \sw of length at most $(n-1)^2$. On the other hand, the best known
upper bound is cubic of $n$. Recently, in the paper \cite{CARPI1} of Alessandro
and Carpi, the authors introduced the new notion of strongly transitivity for
automata and conjectured that this property with a help of \emph{Extension}
method allows to get a quadratic upper bound for the length of the shortest
\sws. They also confirmed this conjecture for circular automata. We disprove
this conjecture and the long-standing \emph{Extension} conjecture too. We also
consider the widely used Extension method and its perspectives.
