MINNEAPOLIS — Adrian Peterson was reinstated by the NFL in April. He rejoined the Minnesota Vikings in June. He even got a new contract in July, with the guaranteed money he was seeking.

From the league’s view, then, there should be no further dispute about the application of the personal conduct policy related to Peterson’s punishment last season. The situation turned out all right for the star running back, now that he’s back on the field.

For the NFL Players Association, there are still legal problems in play. The union argues Peterson should be paid back the millions he lost during what amounted to a six-game suspension, and the league has defied the federal judge in charge of the case.

NFLPA and NFL lawyers traded arguments Wednesday in front of U.S. District Judge David Doty on the union’s contempt of court motion that was filed in May.