How to do 10 G Database recovery without archive logs but available redo logs, ctl files and .dbf files
Alright, let's assume you have full backup without archivelog. And your backup is output from rman backup such as rman&gt; BACKUP DATABASE;.

So, I'll explain how to restore it.

1) Make sure your DBID is same as your database. (Note : this process is used if you have full backup datafiles,controlfiles,spfile, and copy archivelog if you have.)

SQL&gt; SELECT DBID,OPEN_MODE FROM V$DATABASE; (if you can access your database)
RMAN&gt; SHUTDOWN IMMEDIATE;STARTUP NOMOUNT;
RMAN&gt; SET DBID=your_db_id


ex : G:\rman_backup is your backup location.
If you just to restore your controlfile and datafile, ignore process number 1, continue to process 2.

2) Make sure your autobackup location of CONTROLFILE, SPFILE and DATAFILE also ARCHIVELOG ex : "D:\FLASH_RECOVERY_AREA\your_sid\AUTOBACKUP\2016_06_16\O1_MF_S_914709345_CP5HHNCS_.BKP" or"G:\rman_backup\O1_MF_S_914709345_CP5HHNCS_.BKP". 

In this example i assume you have activate your autobackup controlfile, if you don't need to restore your spfile skip this. you can next to restore control file.

RMAN&gt; RESTORE SPFILE TO 'C:\app\Administrator\SPFILESIMKARI.ORA' FROM 'G:\rman_backup\O1_MF_S_914709345_CP5HHNCS_.BKP';
RMAN&gt; SHUTDOWN IMMEDIATE;STARTUP NOMOUNT;
RMAN&gt; RESTORE CONTROLFILE FROM 'G:\rman_backup\O1_MF_S_914709345_CP5HHNCS_.BKP';
RMAN&gt; SHUTDOWN IMMEDIATE;STARTUP MOUNT;
RMAN&gt; LIST BACKUP;
RMAN&gt; CATALOG START WITH 'G:\rman_backup'; -- This is optional, if your control file can show "list backup" you don't need to run this. If not, you must to run this script.
RMAN&gt; RESTORE DATABASE;
RMAN&gt; RECOVER DATABASE;
RMAN&gt; ALTER DATABASE OPEN; -- If you need to reset your sequence, or error you can "alter database open resetlogs", if not "alter database open noresetlogs";
RMAN&gt; exit


For additional information, you can startup unmount if your SPFILE is configured properly. And `startup mount' if your controlfile is configured properly.
Hope this help you out, please comment if you've trouble.