The two machines pictured below are not identical, and they are not isomorphic. Rather, for each move transition in one machine, the other specifies the same transition, just with the oppositve movement. All write transitions are identical. As a result, when one machine moves right, the other moves left and vice versa. It is easy to see that these two machines will be equally as productive but will behave in a mirrored fashion to one another. There is no need, therefore, to consider both machines.

The solution to eliminating mirror machines is actually quite simple. By simply forcing the first move to always be to the right, it is impossible to generate any mirror machines. In addition, the completeness of the search remains in tact because for any machine that would have been produced if its first move was a left, its mirror machine is guaranteed to be enumerated at some point by the tree. Combined with the Empty tape and nonproductive transition filters, this leaves us with the following initial search tree: