Reading the book Practical Foundations for Programming Language.
In section 5.1 Transition Systems, the author said that
Whereas all final states are, by convention, stuck, there may be stuck states in a transition system that are not final.
Thus every complete transition sequence is maximal, but maximal sequences are not necessarily complete.
It seems that in practice a stuck state is always final, but I wonder when is a stuck state not final? (Could you give me an example?)
Also, if we think that the stuck state is always final, it seems no different between maximal and complete?
A transition sequence is maximal iff there is no $s$ such that $s_n \mapsto s$, and it is complete iff it is maximal and, in addition, $s_n$ final.
Also, do the states mentioned here refer to different states? If there is a fixed-point state in a transition system, the state is final or stuck?