I'm gonna solve it by graphing
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You can adjust which values are set to x and y to see the solution space for those values, given your existing values. the solution space is where three of the areas overlap (one from each pair). one should note that at usually least one of the pairs will not depend on x or y, and therefore either cover the entire screen, or not exist. m is also just a buffer, because inequalities are not graphed when one side is undefined. The bigger m is, the larger the values the function is accurate for. (do not make m or m2 negative) it sets the number of turns to beat the opponent to m*opponent's Hp. also this is just for the three character situation (and I used my original three character solution to test it), I plan to make another for the four character one. I also think the second smaller inequalities might be contained in the larger ones, and therefore be irrelevant.
intended solution for RPS:
given the fact one always wins if they takes 0 damage, we can set up R with 1 defense, P with 2 attack and super low hp, S with 1 attack and super high hp
intended solution for ABCD:
given the fact that fight ties if both sides can't damage each other or both sides die in the same turn
we can set up A and C with high defense so that they can't hurt each other
B and D with low hp so that they otk each other
modify their stats to form a loop
I forgot the intended solution for ABCDE