The rolling friction of a car tire - this is caused by the flexing of the
rubber, which is a result of the normal and (probably to a much lesser
extent), the static friction.
As the tire is compressed at the front, the road is acting on the tire,
pushing it up and back**. As the tire recovers, the road is pushing up and
forwards**. All that is required for a rolling friction force is that int
{F dt} over the compression/recovery be non-zero.
Unless the tires are perfectly elastic, I would expect this to be the
case. In this event, "rolling friction" does not appear to be friction at
all, but the effect of a variable normal force.
**Does the back/forwards automatically imply friction? Can a rolling tire
flex on a frictionless surface? Is the plane of contact (at the front and
rear contact points) parallel to the road surface?