Personally I agree more with
@Elfwine. I don’t think Barbarossa surviving and his army participating in the third crusade is the end all be all that’ll so utterly destroy the Muslims and expand the crusader states to the point of the Muslims being unable to invade again as has been suggested. I think if the German army, and the French army (as iirc Phillipe Augustus left after Fredrick died so maybe they’d stay this time?) taking part would’ve made the third crusade a more successful war. I do think the Kingdom of Jerusalem would’ve been restored and possibly gain some minor strategic gains. But I don’t think it would be some end all be all defeat for the Muslims.
Technically, me and Elfwine have lately only been going back and forth on whether Frederick can secure the Orontes (north of Homs) in the ten months he has before the arrival of Richard and Phillip; beyond
that, I would agree the three monarchs working together and settling the leadership of Jerusalem is likely to be enough to restore the Kingdom to its pre-Saladin borders (or at least securing the coast as far south as Asacalom and/or Darum and pushing inland as far as the Dead Sea and Jordan River. After that...
Not unless we see Saladin and his Ayubid dynasty fall, with Egypt and Syria not only soundly defeated by the crusaders but also left in turmoil long enough for the crusader states to catch their breath and if the two never reunite. That’s not impossible but not to the degree as some have said here. And even if Egypt and Syria go through turmoil I don’t see the Muslims being forever pushed back and eventually we will see another round of wars.
There are two major strongholds in Muslim Syria worth noting at this point -- Homs and Damascus. By the time you get as far north as Aleppo, you're practically knocking on the door of Mosul or the Sejuks.
Now, I'm not saying the Third Crusade takes these two major strongholds while also restoring the Kingdom of Jerusalem. But I am saying that, with another crusade down the line, not only could Egypt and Syria be cut off from each other, but "Muslim Syria"
could become
effectively non-existent (notwithstanding Aleppo, etc); Egypt could invade the Kingdom of Jerusalem from the south, and Antioch could be attacked from the northeast (by way of Edessa and Aleppo), but the muslim powers can't fully suround the Crusaders from the due east. Yes yes, those two cities have to actually have to fall first -- but in this scenario, it's something that the Crusaders and the Crusader States could seriously consider.
That's the general direction anyway; getting there is another matter.