First things first, this is a fragmented loop as defined by 716.3, the definition of pertinent game-state is left up to the discretion of the players or the judge if involved. There is plenty of precedence that repeated usage of abilities that make a minor adjustment to the game state are considered loops. Since we have a loop we by extension have a fragmented loop due to having multiple players.
Unfortunately no one is talking about the shortcut employed by the players, which is very important to how the problem gets resolved.
In these instances a shortcut is not allowed unless agreed between players or a few actions have been taken to establish how the loop will function. How the loop begins drastically changes how the overall game will be impacted.
Assuming there are no other pertinent abilities available, it would begin with the active player having the option to activate an ability on the declare blockers step.
If they choose to begin creating mana, the non-active player can bury their loop creating a non-fragmented loop, allowing "infinite pump", similarly every time the active player tried to pump they could repeat that action. An example shortcut is "every time you pump I pump 100 times", since the active player is required to break the loop, this would end with their shade dead.
If they choose to pass, the non-active player would be given the chance. The reverse of the first example would happen. Note that in this case the active player has to break the loop, however since they got to pump before the loop started, this isn't a problem. The non-active player gets an extra pump, but that doesn't matter when the active player already got lots of pumps.
If the non-active player also passes then the two 1/1's kill each other.
Thus unless I am missing something, it is a game of chicken and thus will result in two 1/1's killing each other.