Flight Instructor reported an NMAC event during landing in which a non reporting aircraft neglected to conduct a standard entry into the downwind. The flight Instructor executed an evasive maneuver to avoid a collision.

Narrative

My student and I were on an RNAV approach into ZZZ airport. We called a 10-mile; 7-mile; 5-mile; and 3-mile final call to runway XX. We heard a high wing Cessna state that he was five miles from the south and that he would be overflying the field to enter the left downwind. I had visual on him as he crossed over midfield. He neglected to conduct a teardrop turn into the downwind; deciding to enter straight into the downwind. This alone is not a problem; however; it was at this point that I was on a 3-mile final. Traffic separation was starting to become a mild concern. Again; I was making every call necessary for safety and traffic separation. I had a visual on the aircraft as he was entering the downwind and expected him to maintain visual separation with me. I should point out that this incident is with a low wing aircraft being lower than a high wing aircraft. There was nothing preventing Aircraft Y from visually identifying me while I was on short final. I was 400 ft below him on a 2-mile final; when Aircraft Y started turning base to final. I grabbed the controls from my student and conducted a descending left turn to maintain my visual contact on this incoming aircraft. When he started turning towards me; I started getting alerts from my EFB traffic avoidance system stating that I was within 400 ft of another aircraft. I then made a CTAF call that I was abandoning the approach and departing the area.