Is this NIM game tree correct? I have an assignment to construct a game of Nim (a game in which two players must divide a pile of tokens into two unequal sizes; 6 can be divided into 2 &amp; 4 but not 3 &amp; 3). I was provided a game tree (the same one I find on Google), but I am confused. Shouldn't the first turn of the second player have access to S6, S5, and S4 and S3 since 7 can be divided into 4 &amp; 3?
There are many kinds of NIM. The one in the picture is a rather classic example. Take either one or two tokens, the one who takes the last token looses. 

Does not sound like the version you suggest. Your game does not state what happens with the divided heaps?