tderz Rubilia, I followed your explanation above, thank you for it!
I have a comment, some questions and suggestions:
Comment: above sounds as Black would win the game because Black would be repeating the game position with d after White c.
I think that it's rather the opposite:
Black would win because White illegaly repeated the game position (with her own last & identical move) c. Black could/(should) claim win at this point - no need to play an illegal move himself (d, repeating a board position too).
Hence, the definition of superko ends in the same(?) game position with a different game result (loss for White after the 2nd time c) to above explanation in  (win for White, as she turns to c).
Having the opposing results in mind, is active meant to signify here Anti-superko? (as it does not fall under the genus superko).
So the last one to be in a repeated game sequence of two moves started in a necessarily previously existing game position (same player to move), will win the game under the game rule called here active superko.
This would be active superkos comprising turns with uneven (e.g. 1, 3, 5) numbers.
(Under this rule, you'd start a ko, opponent take, you re-take and win the game; suprising (boring?) isn't it?
Arriving here, I finally got the meaning of turn near the top of this page.
Now I understand, that still the correct side would win, even if only an illegal move (because repetiting too) later. So one still has to think about conflicting Tournament Rules  too.
I am happy to realize that the first one to repeat any game position would lose the game (if turn comprises even numbere of moves), as that is my amateur players understanding of the ko-rule.
Question: Could s.o. explain to me why this second repetition of a game position  (Black d after losing White c) is necessary?
It's my first time to indulge in this rather theoretical, almost juridical superko stuff.
Please apologize any logical mistakes above, as I started shocked by the flawed understanding that the one repetiting with illegal moves could win the game.
Charles Matthew's ko-book is quite complicated too, but of high practical importance.
 In tournaments Go is played under Tournament Rules in addition to Game Rules.
E.g. Go Lightning Tournament Rules often state that the first one to claim a losing action of the opponent (e.g. a fallen time flag) wins the game.
W.r.t. this rule Black should not play d.
blubb: Hello, tderz. Please, see my reply in the forum. Would you mind moving above discourse to /discussion or similar, to be continued there? As far as I can see, it mainly describes a coiled process of understanding active superko (starting from a misconception), rather than its actual properties.