One of the most challenging aspects of English verbs is that the semantics of the verbs can change considerably when using particles. Particles look like prepositions, and function like them to a certain degree, but semantically speaking, they alter the meaning of the verb they co-occur with. In the case of "cheat" vs. "cheat on," for example. "To cheat" means to use some kind of trickery to get something or more of something from someone rather than playing by accepted rules of exchange. "To cheat on." on the other hand, though related in many ways, means you are in a committed relationship with one person and have sex with a different person. You are said "to cheat on" the person you are in a relationship with.
I'm not sure why you are considering whether to leave such things out or not. I'm not sure what you are working out when you do this, but in this algorithm you're working through, put in a component that recognizes that these particles significantly alter meaning and are not dispensable semantically, even if grammatically the sentence still works.