Hi niladri.s.debnath!
It is definitely true that VCS will check setup time and hold time if SDF is annotated and "-notimingcheck" is not used.I've glanced the VCS cmds this morning.
I'm sure, basically, Suppose some violations exist, VCS will give out a waring about them. such as violation types, which path, when it comes out, and whats more signals related to violations will turn to X.
Actually, I didn't try to sim a project with a clk whose period is less than a critical path, course I thought it could give no more than a red "X" or many "X"s.
As for ur design, I think u may check the critical path, where is it, since it is not that complex. Can it be the impossible path?
best regards!