ST. LOUIS (AP) -- The NFL Players Association has submitted its written argument to the 8th U.S. Circuit Court of Appeals, criticizing the suspension of Minnesota Vikings running back Adrian Peterson that has since expired.

The NFL asked the appeals court in its initial filing April 8 to overturn U.S. District Judge David Doty on the grounds he didn't have authority in the league's labor dispute with the union that falls under the umbrella of the collective bargaining agreement.

Peterson was suspended after he was accused of child abuse for using a wooden switch on his young son, a Texas case that was eventually resolved.

The suspension was enacted with six games remaining on Minnesota's schedule. The union's primary argument was that Peterson should only have been subjected to a two-game suspension, since the incident with his son occurred before Commissioner Roger Goodell's announcement of the new policy on domestic violence that upped the penalty to a six-game ban. Peterson played in one game last season, spending much of it on paid leave. Goodell reinstated him April 16.

Doty ruled Feb. 26 that league arbitrator Harold Henderson's denial of Peterson's appeal should be voided, prompting the NFL's turn to a higher court.

In its brief to the court of appeals made public Tuesday, the NFLPA wrote that Doty's decision was ''unassailably correct'' in rejecting Henderson's decision, which ''lacks the hallmarks of an honest judgment.''

According to Michael Gans, the clerk for the St. Louis-based 8th Circuit Court of Appeals, neither side has asked for an expedition of the case though both are seeking clarity on the protocol and fairness of the personal conduct policy. It's on track for a hearing this fall, likely sometime in October in St. Paul, Minnesota.