I was wondering if anyone had advice for the best software/commands to trim a paired-end sequencing library where the sequences are flanked with a pair of asymmetric adapters.

So basically we have a library of 300-1000 bp fragments, then we use Y-shaped adapters to ligate adapter sequence A to one end of the fragments, and adapter sequence B to the other end of the fragments. Then we throw Illumina TruSeq adapters onto both ends and perform paired-end sequencing on the library:

So our sequencing reads would look something like this:

5'-Adapter A-library fragment-Adapter B-3'

OR

5'-Adapter B-library fragment-Adapter A-3'

I thought about using cutadapt but I don't think it can be customized to the point of filtering reads with the logic (5' Adapter A AND 3' Adapter B) OR (5' Adapter B AND 3' Adapter A), or am I mistaken?

I was also considering performing the trimming operations sequentially, i.e. process case 1 (5' Adapter A AND 3' Adapter B), then process case 2 (5' Adapter B AND 3' Adapter A) in a separate operation. Would that be a more practical approach? Thanks in advance for any advice.