Hypothetical first order $|\Delta S|=2$ transitions in the $K^{0}-\bar{K^{0}}$ complex

The influence of a hypothetical CP violating $|\Delta S|=2$ interaction on the time evolution of the $K^{0} - \bar{K^{0}}$ system is investigated. It is shown, that if we were to assume the existence of the superweak-like interaction then this would lead to the conclusion, that there might be observable effects in the masses of the neutral kaons. We address the possibility of experimental observation of these effects and perform a computer simulation of one of the parameters which describe such effects. Instead of the widely used Lee, Oehme and Yang approximation, which is not suitable to considering this kind of interaction we use a formalism based on the Krolikowski-Rzewuski equation.