ARTCC RADAR CTLR ISSUED DSCNT CLRNC THROUGH THE ASSIGNED ALT AND PROX OF XING TFC IN CRUISE ALT. DUE TO SECTOR COMPLEXITY AND TFC VOLUME; RADAR TEAM DID NOT SEE THE POTENTIAL CONFLICT UNTIL THE COMPUTER DETECTED THE ERROR. RADAR TEAM MAINTAINS THAT TFC MGMNT UNIT AND SUPVR SHOULD HAVE INTERVENED TO REDUCE SECTOR TFC COMPLEXITY MORE TIMELY.

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ACFT X; EBOUND AT FL330; HAD BEEN RERTED TO AVOID WX AND WAS FLYING EBOUND ON A WBOUND AIRWAY. ACFT Y; AT FL350 INBOUND TO STL; NEEDED DSCNT TO COMPLY WITH LOA. DURING THE TIME PRIOR TO AND SUBSEQUENT TO THE INCIDENT; I WAS WORKING 25 ACFT -- 8 OF WHICH WERE CLBING; 2 WERE DSNDING; AN ADDITIONAL ACFT WAS CLBING ON A VECTOR; AND 7 MORE WERE DSNDING ON VECTORS. TFC WAS HVY AND COMPLEX. TFC WAS HVY AND COMPLEX. I WAS WORKING WITH A HDOF CTLR AND RADAR ASSOCIATE. ACFT Y HAD NOT YET CLRED ACFT X WHEN I ISSUED DSCNT. OEDP ACTIVATED AFTER ACFT HAD ALREADY PASSED EACH. THERE WAS NO CONFLICT ALERT. DUE TO HVY COMPLEX TFC; ALL 3 CTLRS WORKING THE SECTOR FAILED TO SEE THE CONFLICTION WITH ACFT X AND Y. TFC MGMNT UNIT HAD WARNED THE SUPVR AT XA15 BRIEFING THAT THIS SECTOR WOULD BE BUSY AND TFC MGMNT UNIT HAD ISSUED MINIMAL RESTRS TO ADJACENT CTRS. THIS SECTOR IS ALWAYS BUSY DURING THIS TIME. A MORE AGGRESSIVE TFC MGMNT PLAN IS NEEDED TO PREVENT THIS SIT FROM RECURRING. SUPPLEMENTAL INFO FROM ACN 414482: THE EVENTS OR CONTRIBUTING FACTORS IN THIS ERROR ARE AS FOLLOWS: CHOP WAS OCCURRING WHICH ADDED TO THE COMPLEXITY BY FORCING THE STL ARRS LOWER THAN NORMAL WHICH MADE IT DIFFICULT TO GET THE CVG ARRS DOWN. ALSO; THE CHOP SIT ADDED TO FREQ CONGESTION. THE SECTOR GOT OUT OF CTL DUE TO THE NUMBER OF AIRPLANES AND THE COMPLEXITY. THIS CAUSED US TO SHUT OFF ZAU WHICH PUT THEIR SECTOR OUT OF CTL AND THEN THEY HAD AN ERROR. OEDP ACTIVATED WHICH IS WHAT DREW MY ATTN TO THE ERROR. NEITHER ACFT KNEW OF THE OTHER AND NEITHER TOOK EVASIVE ACTION. THERE SHOULD HAVE BEEN MORE MI IN TRAIL AND MAYBE EVEN ACFT HELD ON THE GND. THE 'BIG SKY THEORY' DOES NOT WORK!