APCH CTLR WORKING COMBINED POS WITH 2 ACR ACFT INBOUND VECTORS ONE OF THE ACFT BEHIND THE OTHER RESULTING IN LTSS. BOTH ACFT REACT TO TCASII.

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WHILE WORKING RADAR ARR N AND S COMBINED; I TOOK 2 HDOFS FROM ZLC; 35 MI S OF BOISE. RWY 28L&R IN USE. THE ACFT ON THE L (W) WAS ACR X. THE ACFT ON THE R (E) WAS ACR Y. THEY WERE APPROX 6 MI APART; BOTH DIRECT TO BOISE VOR AND THE SAME DISTANCE OUT. ACR X WAS ABOUT 14000 FT DSNDING TO 13000 FT. ACR Y WAS ABOUT 16000 FT DSNDING TO 14000 FT. I DSNDED ACR X TO 9000 FT AND THEN (BEFORE 10000 FT) AGAIN TO 5000 FT. I DSNDED ACR Y TO 10000 FT AND TURNED ACR Y L TOWARDS ACR X TO ACHIEVE A SEQUENCE BEHIND ACR X. AT THE TIME I TURNED ACR Y; I THOUGHT ACR X WAS LEAVING 10000 FT (ACR Y WAS AT ABOUT 11500 FT AT THAT TIME) AND I CALLED ACR X TFC TO ACR Y AND TOLD ACR Y THAT ACR X WAS LEAVING 10000 FT. AFTER TALKING TO ANOTHER ACFT; I LOOKED BACK TO DISCOVER THAT ACR X WAS LEVEL AT 10000 FT AND ACR Y WAS ABOUT 3 MI AWAY; CLOSING AND AT 10500 FT. I TOLD ACR Y ABOUT THE TFC AGAIN AND TOLD ACR Y TO CLB AND MAINTAIN 11000 FT. IMMEDIATELY AFTER THAT XMISSION; ACR X ADVISED THAT HE HAD AN RA AND WAS CLBING IN RESPONSE. I THEN WENT RIGHT BACK TO ACR Y AND ADVISED HIM THAT ACR X WAS CLBING AND THAT INSTEAD OF CLBING THAT ACR Y SHOULD DSND. I THEN RESUMED NORMAL OP AFTER THE ACFT WERE 1000+ FT; VERTLY SEPARATED AND NOTIFIED THE SUPVR OF WHAT HAD HAPPENED. SUPPLEMENTAL INFO FROM ACN 348096: ACR X ARRIVING BOI FROM S; WHILE ACR Y ARRIVING FROM SSE ABEAM EACH OTHER ON CONVERGING COURSES WITH ACR Y AT HIGHER ALT ON OUR R. BOI LNDG W. BOI APCH DECIDED WE WOULD BE #1 ACCOUNT LOWER AND CLRED US FROM 14000 FT TO 9000 FT AND KEEP SPD UP. ACR Y CLRED TO 10000 FT. APPROX 18 MI S BOI AT 10100 FT SLOWING; I SAW TCASII TARGET CLOSING FROM 3 O'CLOCK. I CHANGED TO 10 MI SCALE TO CHK SEPARATION AND NOTED 3 MI AND CLOSING AT 10000 FT. I ADVISED FO (FLYING) OF TFC CLOSING AT 3 O'CLOCK AND AS I FINISHED THE REMARK; WE GOT A TA FOLLOWED SHORTLY BY AN RA CLB. FO REACTION WAS VERY PROMPT. I RPTED RA CLBING TO ATC. ONLY AFTER ATC REPLY DID ACR Y RPT RA AND BEGIN DSCNT. DISPLAY SHOWED ACR Y SLOW TO LEAVE 10000 FT. WE CLBED ABOVE 11500 FT TO STOP THE RA. LATER PERSONAL CONTACT WITH ACR Y CAPT REVEALED HE SAW 200 FT SEPARATION ON HIS TCASII. HE SAID HE WAS ON 350 DEG HDG. WE WERE DIRECT BOI (APPROX HDG 010 DEGS). WIND STRONG FROM NW. PHONE CALL TO TWR SUPVR AND APCH CTLR REVEALED CTLR HAD NEGLECTED OUR SLOWING AT 10000 FT AND CONVERGING TRACKS. HE SAID HE SHOULD HAVE CLRED ACR Y ONLY TO 11000 FT. HE SAID IT WAS HIS FAULT AS HE HAD DIVERTED HIS ATTN TO ANOTHER ACFT. WE MISSED ONLY BECAUSE OF OUR 10100 FT SLOWING AND VERY PROMPT RA RESPONSE BY FO. WE COULD NOT READ TCASII ALT INFO AT INSTANT OF RA BECAUSE IT WAS OBSCURED BY OUR ACFT SYMBOL. OUR NOTICE OF TFC PRIOR TO TA CERTAINLY HELPED OUR RESPONSE. SIMPLY FLYING OUR OWN ACFT IS NOT ADEQUATE; WE MUST ALWAYS HAVE PART OF OUR MIND FUNCTIONING AS A CTLR. SUPPLEMENTAL INFO FROM ACN 347799: ACR X 'DSND TO 4000 FT' FROM 10000 FT. KEEP YOUR SPD UP #1 TO THE ARPT. MY INSTRUCTIONS WERE TO DSND TO 10000 FT TURN L TO 360 DEGS TO FOLLOW ACR X. WE BOTH ENTERED THE CLOUDS AT 10000 FT. SOON THEREAFTER WE BOTH GOT AN RA ON THE TCASII. WE BOTH REACTED TO THE RA TO AVOID THE CONFLICT AT 10000 FT. THE CTLR ASKED THE ACR X WHY HE DIDN'T DSND TO 4000 FT. HIS RESPONSE WAS THAT HE HAD TO LEVEL AT 10000 FT TO SLOW DOWN; PUTTING BOTH OF US AT 10000 FT. THE CTLR HAD 2 AIRPLANES IN HIS SPACE AND HE ALMOST BROUGHT THEM TOGETHER. I FEEL HE WAS ASLEEP AT THE WHEEL. BOTH AIRPLANES DID WHAT THEY WERE TOLD OR BY FARS.