"you can't get owt for nowt"
Interesting,.... but your logic is flawed.
You are actually putting something in: WATER
The water is used up and is therefore a supplementary "fuel" in this case.
Also any auto electrician will tell you that an alternator puts out approx 17 volts,.. where the battery only uses 12,.. so it is this wasted voltage that is used to split the water,... making the system less wasteful, but not breaking any law of thermodynamics!
So,... the question is,... in real life, taking in to account all the inefficiencies and energy losses:
Does it actually make any difference at all to your fuel consumption???
I want to hear from someone who has actually tried it,... not a 3rd party who thinks they know about it!!
Are there any "run your car on water" forums???