What was found
AT CRUISE ALTITUDE 3 HOURS INTO FLIGHT WITH A/P "A" SELECTED THE LEFT FMC FAILED AND CAPTAIN NAV DISPLAY SHOWED VTK, A/P "A" STOPPED FUNCTIONING, FMA WENT TO HEADING HOLD AND ALTITUDE HOLD. WE SWITCHED TO A/P "B" AND REGAINED LNAV AND VNAV FROM RIGHT FMC. CAPTAIN FMC ONLY DISPLAYED ACARS, ACMS AND CAT FROM THE MENU PROMPT. AFTER 30 SECONDS THE LEFT FMC BEGAN FUNCTIONING CORRECTLY AND WAS NORMAL THE REMAINDER OF THE FLIGHT. GROUNDED - YES. NO HISTORY-PERFORMED B737-800 FIM 34-61 TASK 836 LEFT AND RIGHT FMC'S NORMAL OK FOR SERVICE.