It is only an assumption on your part that your washout period is sufficient. This assumption should be examined.
I would advise that you examine whether there are differential mean values for trial 1 at time t depending on whether trial 1 was the first experimental treatment that the subject received or whether trial 1 was the second experimental treatment. Obviously, you would want to do the same for trial 2. And, while you are at it, you might just as well look at the difference between trial 1 and trial 2 for the two different presentation orders. If there are no differences in any of these effects, then you can ignore the period effects. But I wouldn't just assume that you can ignore the period effects.
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