What was found
LEFT FMC FAILED TWICE IN 15 MINUTES DURING CRUISE FLIGHT. SELF-RESOLVED BOTH TIMES, COULD NOT MODIFY ROUTE AFTER. SELECTED FMC BOTH ON RT IAW QRH FMC FAIL CHECKLIST, RESOLVED THIS PROBLEM. NOTE THAT AFTER RESOLVING, THE LEFT FMC DID HAVE A POSITION ON POS SHIFT 3/3 BUT WAS STILL CAUSING A CONFLICT. ACFT GROUNDED. PERFORMED FIM 34-61, TASK 836 AND LT FMC OPS NORMAL. GROUND FUNCTIONAL CHECKED GOOD.