I'd like to know if infinitely repeating sequences of moves (i.e. cycles) are possible in the following game:
Prodway 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 or on a point occupied by an enemy stone. In the latter case, move the enemy stone to an orthogonally adjacent empty point before placing your stone. Your newly placed stone must not be part of any crosscuts. If the moved enemy stone is part of one or more crosscuts, remove the other enemy stones in those crosscuts.
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.
Here's a mesmerizing near cycle (ignoring the win condition):
Reneo, a related game, is finite, but has different rules for swaps and removals. In Prodway, captures are more frequent, and you can capture up to two enemy stones on a single turn. In Reneo, you never capture more than one stone on a single turn.