GSP APCH CTLR DESCRIBED SEPARATION LOSS AT 7000 INVOLVING TWO OVER FLIGHT ACFT; FAA RECORDED POSSIBLE OPERROR AND PLTDEV.

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I WAS WORKING COMBINED RADAR POS. WX HAD BEEN LOW IFR WITH RVR VALUES JUST ABOVE MINIMUMS; BUT WAS IMPROVING TO VFR. I HAD RESPONSIBILITY FOR FINAL AT GSP PLUS 5 OTHER SMALL GA ARPTS. TFC WAS VERY HVY. I HAD BEEN IN THE POS ABOUT 1.5 HRS BEFORE I FAILED TO NOTICE THE CONFLICTIONS OF THESE 2 OVERFLT ACFT. I ISSUED TFC ALERTS AND TURNED BOTH ACFT TO OPPOSITE HDGS. I LOST SEPARATION BEFORE THE ACFT WERE ON DIVERGING HDGS. STAFFING WAS SIMPLY NOT ADEQUATE FOR THE TFC AND COMPLEXITY. I WAS WORKING 2 SECTORS COMBINED. ONE OF THE ACFT INVOLVED IN THE ERROR WAS NOT FLYING THEIR FILED RTE OF FLT. TFC WAS SO HVY AND COMPLEX THAT I HAD BECOME REACTIONARY IN MY CTLING. I WAS INVOLVED WITH A TURN TO FINAL OF A REGIONAL JET AND A MISSED APCH OF A C210; WHILE I WAS COORDINATING WITH 2 NEIGHBORING APCH CTLS FOR A POINTOUT OF OTHER OVERFLT ACFT. MGMNT IS VERY PROUD OF HOW LITTLE OVERTIME THEY USE. HOWEVER; CPC STAFFING IS DOWN TO 13 AT THIS VERY COMPLEX APCH CTL. ALL OF OUR EQUIP IS AT LEAST 35 YRS OLD WITH MANY ANOMALIES THAT CANNOT BE FIXED DUE TO THE AGE OF THE EQUIP.