Very interesting game. Sure opens the floodgates about the complexity of time travel and its consequences. Let's say for example I go back and try to prevent the assassination of a prominent figure (MLK, Kennedy, etc.) That's great you saved a person's life, but the major issue that this will cause a terrible time loop as there would be no purpose to travel back in time, but then the vicious pardox begins.
Are you really traveling back in time to alter history? Or are you just going back in time to erase your existence? I'm telling ya, so many questions on the moral, ethics and technicalities of time traveling.