Memorylessness of simple delay system
A system is memoryless if its output ($y(t)$) for each value of the independent variable ($t$ in this case) at a given time is dependent only on the input at that same time ($x(t)$).

Every system that consists of a delay (like the one in your example) or an accumulator, for example, are systems with memory.

This can be seen just by replacing $t$ by some number. Take, for instance, $t=0$. In that case, the output for that instant ($y(0)$) depends on the input for another value of the independent variable ($x(C),C&gt;0$); that means that the system has memory.