finding sequences from small length sequences

finding sequences from small length sequences

I want to generate a space by using some events in a specific format. Let
me explain the problem on a small example.
Assume that I have the events a,b,c,d,e,f. I will have 3-length sequences
as an input consisting of these events. From these sequences I want to
generate 6-length (number of events) sequences and there will be no
repeated elements in the sequence, i.e. every event will be used exactly
once. 6-length sequences need to satisfy some rules.(explained on example)
Example:
Input:
list1:['a','b','c']
list2:['c','d','e']
list3:['b','c','d']
list4:['a','c','g']
list5:['f','g','e']
List1 describes that, b and c will come after a, and c will come after b
in the 6-length sequence, i.e, when the order changes sequence also
changes. In the same manner List2 describes that d and e will come after
c, and e will come after d. All of the lists will be taken and rules are
recorded. After all rules extracted from these sequences, I need to
generate 6-length sequence that obeys rules. As an example;
Lets say in our case(for simplicity) inputs are List1,List2 and List3
Input:
list1:['a','b','c']
list2:['c','d','e']
list3:['b','c','d']
Then some results for these lists are;
['a','b','c','d','e']: it obeys all of the rules from extracted these 3
lists, like b and c comes after a, d and e comes after c, c and d comes
after b. Ýmportant note from here, if c needs to come after a, they do not
need to be adjacent in the output sequence(6-length)
It is not guaranteed that 6-length sequence will always exist. Firstly, it
needs to be checked that there is at least one such sequence. If not,
algorithm should return false. As an example; lets assume our inputs are
Lis1, Lis2, Lis3, Lis4 and Lis5.
Input:
list1:['a','b','c']
list2:['c','d','e']
list3:['b','c','d']
list4:['a','c','g']
list5:['e','g','b']
a => b => c => g => b it is not possible since b can not come after itself.
I need an algorithm to generate these sequences in Python. I do not have
any code for now, because so far I could not think any efficient
algorithm. It needs to be very efficient in finding longer length
sequences, too.
If the question is not clear, please let me now.
Thanks