Date: 202107
Local time of day: 1201-1800
Location: ZZZ.Tower, US
Flight conditions: VMC
Weather elements / visibility: 6
Light: Daylight
Aircraft: Skyhawk 172/Cutlass 172
Operator: Personal
Operating under: Part 91
Flight plan: None
Mission: Training
Flight phase: Landing
Airspace: Class D ZZZ
ATC / advisory: Tower ZZZ
Second aircraft: Small Aircraft; High Wing; 1 Eng; Fixed Gear
Reporter organization: Personal
Reporter function: Single Pilot
Reporter qualification: Flight Crew Student
Human factors: Situational Awareness; Communication Breakdown
Second reporter function: Local
Anomaly: Conflict NMAC; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Detector: Person Flight Crew; Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Separated Traffic; Air Traffic Control Issued New Clearance; Air Traffic Control Provided Assistance; Air Traffic Control Issued Advisory / Alert; Flight Crew Took Evasive Action
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: In an extremely busy pattern on both sides of ZZZ's Runway XX; 2 planes (Aircraft Y and another- Aircraft Y might have been the lead flight in a flight of two; which I thought were normally not allowed at ZZZ) are given instructions by ATC to extend their right downwind and not turn base due to incoming straight in traffic (my airplane; Aircraft X). Aircraft Y seemingly acknowledges instruction; reports myself in sight; then turns base contrary to instructions. Aircraft Y is at this point 100-200 ft. above Aircraft X; and enters Aircraft X's field of view high and crossing to the left.ATC spots the deviation right as I did; and issues instructions to Aircraft Y to proceed and enter a left downwind.Aircraft Y then turns right- and begins entering final when ATC again contacts Aircraft Y to issue corrective action.During this time I have expedited my descent by going engine idle and adopting a slightly nose down attitude. Due to low AGL; nearby towers and already having 20 degrees of flaps in; I am hesitant to enter a forward slip and descend faster (aircraft type placards state to avoid forward slips with flaps). It's possible that I'm also reaching the end of my endurance- coming back from an hour of pattern practice at ZZZ1 where conditions were gusty. My flight time at this point was around 1.6 hours; and my flights up to that point at typically max of 1.8.I have debated if I should have immediately turned right or even left. While I had the right of way (a lower craft engaged in landing); the right of way isn't going to help me if I end up in a midair. In the end I think it was correct not to turn- the pattern was extremely busy; there were higher towers to the right and planes on extended down wind to both sides. I could have caused another NMAC by turning suddenly. ATC was aware of the situation; issuing instructions to Aircraft Y and I was going to pass safely- although close- below.While I pass under (300-400 ft. estimated?) Aircraft Y either completes a right 360 or an S-turn; and ends up in an extended left downwind.Because I am below the ideal approach path to Runway XX; I put power in and arrest my descent. I actually end up too high for the runway and decide to do a go around. The go around is uneventful and I land safely. I believe Aircraft Y actually landed in between my go around and actual landing.


Second narrative: Moderately heavy traffic relative to ZZZ; training in progress; everything under control of the Trainee until I noticed an aircraft turning base without any sequence or landing clearance yet. This aircraft was initially part of a flight of two who had just separated in the downwind; because we have to issue separate landing clearances at ZZZ; the AID (Aircraft IDentification) is Aircraft Y. Multiple inbound aircraft on either downwind and on straight in.I key up and say 'Aircraft Y and flight; both of you guys; Don't come in on base; there is traffic at the [VFR reporting point]; so don't come in on base right now; you are going to follow the guy on a 3 mile final' The [VFR reporting point] is 3 mile final; Aircraft Y is starting a 1 mile right base so this is plenty of time to catch and correct this pilot. The second aircraft from the original flight of two responds traffic in sight and immediately corrects back to the downwind. I respond to 2 other calls then scan back to ensure Aircraft Y was correcting; he wasn't; I say 'Aircraft Y it looks like you are doing exactly what I said not to do; unless the radar is deceiving me here.' Pilot responds 'Aircraft Y was already on base'; I respond 'OK; well I just said don't go on base; you missed that part; so let's go right turn back to the north downwind for both you and the other guy (his flight wing man; who was following instructions)' Pilot responds 'Affirm; right turn; north downwind; Aircraft Y'. I tell the original wing man to now turn base; he correctly responds; I then scan back and see Aircraft Y not following instructions; again the pilot does the opposite and starts a left turn towards final before correcting right and continuing for the north downwind. I then say 'Aircraft Y are you literally on final right now cutting someone off?' Pilot responds 'No; I'm trying to get out of here; we're turning; Aircraft Y'I advise the traffic on final 'Aircraft X; the guy in front of you is moving out of your way; Runway XX cleared to land' His response seemed to be partially blocked but I heard 'Aircraft X'.All aircraft eventually land; brasher warning was not issued. The pilot of Aircraft X called the tower a couple hours later and said he wanted to file a NMAC. He said he was aware of the situation developing and heard the controller (me) several times tell the other aircraft not to turn base and issue instructions which the pilot of Aircraft Y repeatedly disobeyed. I should have issued a traffic alert to both aircraft; but at the minimum to Aircraft X.


Synopsis: Pilot and Controllers reported a NMAC