Maybe I wasn't clear.

• The order of variables in the output string had to be the same as the input string.

This means that

(abc)(b-ac)
[download]

and

(cb-a)(bca)
[download]

are equally correct input strings (they are even the same expression since (a AND b AND c) OR (b AND NOT a AND c) is the same as (c AND b AND NOT a) OR (b AND c AND a)).

But the output of the first reduction would be

(bc)
[download]

and of the second reduction

(cb)
[download]

Of course there can be many negated variables like this:

(-a-b-c-d)(-c-da-b)
[download]

which would result in

(-b-c-d)
[download]