A problem with the attitude control of the lunar module

The logical command interface of the RCS (lateral thrusters) was controlled with 3 commands of rotation, either positive or negative, and 3 commands of translation, either positive or negative.
So there should have been a channel with 12 bits to send commands to this interface.
Instead of that, there are two channels, with 8 bits each, to send commands to the RCS, so which in fact are theoretically able to individually control the 16 thrusters of the RCS; in reality the LGC does not allow to individually control the thrusters of the RCS, so these commands cannot be used.
Moreover, the program which controls the attitude of the lunar module does not even write into these channels, it does plenty of calculations which are completely useless, as it does not send the result of these calculations to the LGC.
And many of the instructions which are used in this program are even illegal (two macro-instructions on the same line).
And the cherry on the cake is that each vertical command activates two vertical thrusters directly opposed to each other on the same cluster, which thus mutually cancel these respective effects.
So, while we have already seen that the AGC was not able to control the thrust of the main engine, we now see that it is no more able to control the lateral thrusters of the RCS, which was making both the powered descent and the powered ascent impossible.
Nobody ever walked on the moon.
Link to the hand manual of the lunar module:
http://www.hq.nasa.gov/alsj/LM10HandbookVol1.pdf
Link to the program of the control of attitude of the lunar module:
https://www.ibiblio.org/apollo/listings/LUM99R2/ATTITUDE_MANEUVER_ROUTINE.agc.html