What is the definition of half duplex?Is this system,$A$ give $x$ to $B$,then $B$ give $x$ to $C$,called half duplex? I saw the definition of half duplex in wiki,and it said 

half-duplex (HDX) system provides communication in both directions, but only one direction at a time (not simultaneously). Typically, once a party begins receiving a signal, it must wait for the transmitter to stop transmitting, before replying.



However,i saw a paper: http://jultika.oulu.fi/files/nbnfi-fe2019040110636.pdf ,its system model is a transmitter transmit the $x_1$ and $x_2$ information to the user1(U1),then U1 transmit $x_2$ to the user2(U2),and it said this is half-duplex.

So in fact,the definition of half duplex is that device can transmit and receive,but no need to transmit and receive at the same time?

I mean,$A$ give $x$ to $B$,then $B$ give $x$ to $C$,this is also called half-duplex?I thought this is called simplex duplex before,because i thought the half-duplex is $A$ give $x$ to $B$,then $B$ give $x$ back to $A$.

So i want to ask that $A$ give $x$ to $B$,then $B$ give $x$ to $C$,this is also half-duplex?
The receiver/transmitter pair in B's possession is operating in half-duplex mode.  


As you say "$A$ give $x$ to $B$, then $B$ give $x$ to $C$" which specifies that while $B$ ls listening to what $A$ is telling it (the $x$ that is being given to $B$), the transmitter in $B$'s possession must remain silent until $B$ has completely received $x$. It is only then that $B$ can start up his transmitter and send $x$ to $C$. So, $B$ cannot receive and transmit at the same time, that is, $B$ is operating in a half-duplex mode. If $A$ were to send $y$ to $B$ while $B$ is sending $x$ to $C$, $B$ just ignore the transmission from $A$: $B$'s transmitter is active and so its receiver must be in-operational till $B$ is done talking to $C$.