A BE02 FLC; THINKING THAT THEY HAD BEEN CLRED FOR THE ILS RWY 25 APCH INTO FMN; NM; LEAVES THEIR ASSIGNED ALT OF 10000 FT FOR 8500 FT. FLT HAD BEEN CLRED; 'VIA THE 10 DME ARC S TO ILS RWY 25 INTO FMN.' CTLR ASKED THEM THEIR ALT AND AFTER SAYING THEY HAD NOT BEEN CLRED FOR THE APCH; GAVE APCH CLRNC.

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NIGHT; IFR CLRNC OUT OF DRO; FLEW PUBLISHED IFR DEP PROC OUT OF THIS NON TWRED ARPT (ON WAY TO FMN). CHKED IN WITH ZDV AT 10000 FT MSL (OUR ASSIGNED ALT). DIFFERENT CTLR VOICE THIS TIME (FEMALE). SHE ASKED WHAT APCH WE WANTED INTO FMN (SINCE IT WAS PARTIALLY IFR/VFR AT NIGHT). I; AS PNF; REQUESTED THE 10 DME ARC S TO THE ILS RWY 25 INTO FARMINGTON. SHE THEN SAID 'CLRED VIA V95 TO THE 10 DME ARC S TO ILS RWY 25 INTO FARMINGTON.' SHE MAY HAVE SAID MAINTAIN 10000 FT BUT NEITHER THE CAPT OR I CAN RECALL. WE FLEW V95; ENTERED THE 10 DME ARC WHERE PUBLISHED ALT ON IT IS 8500 FT MSL. WE STARTED TO DSND ON DOWN TO 8500 FT AND I CHKED IN WITH ATC AT 9500 FT WHILE DSNDING TO TELL HER WE WERE ON THE 10 DME ARC. SHE ASKED US IF WE WERE DSNDING. I SAID WE WERE DSNDING TO 8500 FT. SHE SAID WE WERE NOT CLRED FOR THE APCH AND THEN SHE CLRED US FOR THE ILS RWY 25 FMN. CAPT AND I UNDERSTOOD LAST CLRNC AS OK TO DO APCH. IT WAS SOMEWHAT AMBIGUOUS. THIS WAS OUR 11TH LEG OF THE DAY. WE WERE TIRED (FLEW FROM XB00 TO XP00) WITH ONLY TWO BREAKS ALL DAY. WE LANDED SAFELY AND DID THE APCH WITH NO PROBS. WE BOTH ASSUMED AND CHKED WITH EACH OTHER THAT WE WERE CLRED FOR APCH BUT DID NOT VERIFY WITH ATC. SUPPLEMENTAL INFO FROM ACN 389408: DAY WAS THE END OF A 5 DAY TRIP THAT INCLUDED; A NEW FO AND MANY APCHS DUE TO A STALLED LOW PRESSURE SYS OVER THE SW; WITH A SCHEDULED FLYING TIME OF 7 HRS AND 54 MINS; JUST 8 MINS LESS THAN THE LEGAL 8 HRS; NOT TO MENTION A DUTY TIME OF 13 HRS AND 25 MINS. THIS DAY THE FLT TIME RAN INTO 9 HRS AND 20 MINS WITH A DUTY DAY EXTENDING WELL PAST 15 HRS. ADD THE HOTEL SHUTTLE AND STRESS; WE WERE VERY TIRED. WE SHOT 9 ILS APCHS OUT OF 11 TOTAL LEGS. THE CTLRS WERE SHORT STAFFED AND WORKING MANY ACFT. OFTEN WE WENT FROM CTR TO TWR AND SIMPLY SKIPPED APCH CTL. I BELIEVE WE WERE LULLED INTO A FALSE SENSE OF JUST EXPECTING OUR CLRNC.