Kopczy\'{n}ski (ICALP 2006) conjectured that prefix-independent half-positional winning conditions are closed under finite unions. We refute this conjecture over finite arenas. For that, we introduce a new class of prefix-independent bi-positional winning conditions called energy conditions over totally ordered groups. We give an example of two such conditions whose union is not half-positional. We also conjecture that every prefix-independent bi-positional winning condition coincides with some energy condition over a totally ordered group on periodic sequences.
翻译：Kopczy\\{n}ski (CICLP 2006) 推测前等独立半场赢赢的条件在有限结合下是封闭的。 我们驳斥了这种对有限场场场的推测。 为此, 我们引入了一种新的先等独立双场赢条件, 称为对完全定购组群的能量条件。 我们举了两个这样的条件的例子, 它们的结合不是半场的。 我们还推测, 每一个前等独立双场赢条件都与一个完全定购组的周期性组合的能量条件相吻合。
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