Eventually, the sun will run out of hydrogen, a whole bunch of physics stuff will happen, and the Earth will be nothing more than a lifeless rock tumbling through what's left of our solar system.

At that time, if nothing else, yes, the war in Syria will end. However, this is no guarantee that the Syrians will not pack up all their things and relocate to another planet, call it New Syria, and continue their war.

Even if Assad is defeated, this won't mean the rebels will form a democratic government. It won't even be as nice as Egypt where a single group took power. It will be like Afghanistan or Iraq, where the removal of a strongman will cause complete anarchy. The rebels will split along tribal and religious lines and begin fighting each other for territory. It will be worse than right now.

Well technically depending on what theory of time you absrcibe to, even if they were all to get wiped out it wouldn't end.

Thats exactly what Europe was like, protestants fighting catholics about 300 to 500 years ago (still a problem in Northern Ireland!) It might end in the Arab world, if they ever have enough of conflict, like we Europeans did. 

The war is heading to a close, or at least this phase of the war (hopefully the only phase) is ending this year for many reasons:

The government has lost control of about 60% of the country at this point.

Their monetary reserves are running low to pay soldiers, mercenaries and thugs.

The rebels are very close to both the Aleppo and Damascus airports which are vital for the survival of the Assad regime.

The opposition is finally acquiring half decent anti-air weaponry and has been on a campaign of taking over air bases for the last few months that has brought major results. Once the air power of the government is a much reduced factor, the rebels can organize better and finish the fight in Aleppo and Damascus. There's an attack right now on an airbase in Idlib province by the Al Nusra Front.

How do you know this? It's a possibility but no one knows what will actually happen. The rebellion in Lybia was also heavily armed and though there are still security issues it's a lot less violent than during the revolution. Countries like Turkey and Saudi Arabia will come in to try and make sure the civil war ends after the fall of Assad because the country is too important for them.