SMA Y HAD NMAC WITH SMA X ON FINAL APCH. SEE AND AVOID CONCEPT.

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I WAS WORKING LCL CTL 1 POS FROM XA17 TO XC36. CTLR TRAINING WAS IN PROGRESS AT THE LCL CTL 1 POS. (TRAINEE) HAD INSTRUCTED SMA X TO MAKE A STRAIGHT-IN APCH TO RWY 25L -- TO RPT A 4 MI FINAL. X WAS ADVISED OF NUMEROUS ACFT INBOUND FROM THE E. DUE TO RADIO FREQ CONGESTION AND OVERLAPPING RADIO XMISSIONS -- I ASSUMED LCL CTL POS RESPONSIBILITY. AT APPROX XC12Z I HEARD SMA Y CALL 'ENTERING DOWNWIND FROM THE HILLS.' THIS WAS THE FIRST RADIO CALL RECEIVED FROM Y. DUE TO THE POOR QUALITY OF THE RADIO; I ASKED Y TO 'SAY AGAIN AND TO GIVE HIS POS FROM THE ARPT.' Y REPLIED 'W OF THE ARPT.' I INSTRUCTED Y TO 'ENTER R TFC; RWY 25R; RPT ON THE 45 TO DOWNWIND.' WITHIN 5-8 SECONDS Y RPTED ON THE 45 TO DOWNWIND. I DID NOT OBSERVE Y ON A 45 TO R TFC NOR IN THE L HAND PATTERN. I MADE A RADIO XMISSION TO Y ADVISING 'NOT IN SIGHT; RPT MID-FIELD ON DOWNWIND.' TIME PASSED; Y WAS NOT OBSERVED ON R DOWNWIND. MY SCAN IMMEDIATELY SHIFTED TO THE L PATTERN; Y WAS NOT IN SIGHT. I ASKED Y IF HE HAD PASSED MID-FIELD ON DOWNWIND? Y STATED IN A VERY GARBLED MANNER WHAT SOUNDED LIKE 'AFFIRMATIVE' -- THE REST OF HIS RADIO CALL WAS NOT READABLE. Y WAS NOT IN SIGHT. X RPTED THE 4 MI FINAL FOR RWY 25L. Y CALLED 'BASE TURNING FINAL.' NO ACFT WAS OBSERVED ON R BASE TURNING FINAL. A QUICK SCAN TO THE L PATTERN PRODUCED SIGHT OF A TWIN-ENG ACFT Y TURNING FROM L DOWNWIND TO L BASE. Y WAS BANKED TO THE L AND WITHIN 2 SECONDS HAD PASSED THE INBOUND CESSNA X. NO TIME FOR A TA SO I ASKED Y IF HE WAS TURNING L BASE. Y ANSWERED 'AFFIRMATIVE.' I COULD NOT DEFINE IF Y PASSED IN FRONT OF; OR BEHIND X. I ADVISED Y; YOU WERE ISSUED R TFC; CLRED TO LAND; RWY 25R; FULL STOP. RADIO XMISSIONS FROM Y WERE DIFFICULT TO INTERPRET IN THE STERILE ISOLATED RECORDER-PLAY BACK ROOM AND WERE EVEN MORE DIFFICULT TO UNDERSTAND IN THE CTL TWR CAB.