heuristic approach is to play a timed game in which the player in white moves along ${{A}_d}$ and tries to maximize her wins, while the player in black moves along ${{B}_d}$ and tries to minimize his losses. The players start from the initial vertex of each graph. Then white makes a move by jumping to a vertex in ${{A}_d}$ with transition label $a$, followed by a move of black on an edge in ${{B}_d}$ with the same label $a$. Next, white moves on an edge with label $a'$, followed by a move of black with the same label $a'$ and so on. At each move we record the time difference between the absolute time duration of the paths along ${{A}_d}$ and along ${{B}_d}$. The problem is that we may return to the same pair of locations $(q,q') \in {\mathcal{Q}}^{{{A}_d}} \times {\mathcal{Q}}^{{{B}_d}}$ but with a different time difference between the path along ${{A}_d}$ and that along ${{B}_d}$. In addition, there are moves to locations where the time is not a single value but of the form $t \geq m$. Thus, the game may not be of finite type. One strategy to cope with the complexity of the game is a greedy 