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for people without directional tread, a better way to rotate is to put the front left to the rear and same with the right side.
now, take the left rear and put it on the right front and the right rear on the left front.
(this way is for non-directional tires and gives you a better even and overall tread wear)
in my experience this method require more effort than it is worth for minimal results, unless you have some crazy disorder that only allows you tot make left turns, then by all means do this, but honestly the big difference in wear is bewtten the front and the rear, not on the sides.
cross rotating tires to different sides is never a good idea, believe me, I work in a tire shop.
Actually it's a great idea... sans the fact that a lot of tires are directional and can't be swapped side to side anyway- in which case you're right. Otherwise you're painfully wrong.-- I personally just wouldn't use my time swapping them side to side.