In constraint-based mining, the monotone and anti-monotone properties are exploited to reduce the search space. Even if a constraint has not such suitable properties, existing algorithms can be re-used thanks to an approximation, called relaxation. In this paper, we automatically compute monotone relaxations of primitive-based constraints. First, we show that the latter are a superclass of combinations of both kinds of monotone constraints. Second, we add two operators to detect the properties of monotonicity of such constraints. Finally, we define relaxing operators to obtain monotone relaxations of them.