Decision tree vs. linearly separable or non-separable pattern

As a part of a series of posts discussing how a machine learning classifier works, I ran decision tree to classify a XY-plane, trained with XOR patterns or linearly separable patterns. Its decision boundary was drawn almost perfectly parallel to the assumed true boundary, i.e. Awful result, it appears to never follow the true boundary. Just a little improved, but it still appears to be overfitted. Even worse... it appears to get more overfitted than the case of 2-classes.