I'd like to know if infinitely repeating sequences of moves (i.e. cycles) are possible in the following game:
Reneo is a game for two players (Black and White) that is played on an initially empty square board. The top and bottom edges of the board are colored black; the left and right edges are colored white.
A crosscut is a 2x2 area containing two diagonally adjacent black stones and two diagonally adjacent white stones.
Black plays first, then turns alternate. On your turn, place a stone of your color on an empty point. If this stone is part of a crosscut, swap it with an enemy stone that is also part of the crosscut. As a result, the swapped friendly stone must not be part of a crosscut any more. If the swapped enemy stone is still part of a crosscut, remove that stone.
You win if, after a full move by either player, there is a chain of orthogonally connected stones of your color touching the two opposite board edges of your color. Passing is not allowed, but, if you have no legal moves available, your turn is skipped.
Note that you will never remove more than one stone on a single turn, and you can only remove a stone by placing in the center of this pattern:
o x x · o o x
("x" are black stones, "o" are white stones and "·" is an empty point.)