By Brian Murphy

St. Paul Pioneer Press

NEW YORK — Adrian Peterson’s appeal of a season-ending suspension was adjourned Tuesday following a three-hour hearing in New York, with additional testimony scheduled and time dwindling for the exiled Vikings star to play again in 2014.

Arbitrator Harold Henderson ordered NFL executive vice president of football operations Troy Vincent to appear Thursday and testify about the league’s decision to place Peterson on the Commissioner’s Exempt List earlier this season, according to Pro Football Talk.

ESPN reported that the NFL Players Association, which is fighting to reinstate Peterson, presented Henderson with a transcript and recording of a telephone conversation between Vincent and Peterson. Allegedly, the league executive assured the Vikings running back he would get credit for “time served” on the exempt list, plus a two-game suspension.

The NFL suspended Peterson on Nov. 18 for the rest of the season for violating its personal conduct policy after he plea bargained a felony child abuse charge in Texas down to misdemeanor reckless assault.

Commissioner Roger Goodell, who harshly criticized Peterson’s decision to use a switch to whip his 4-year-old son, ordered the 2012 MVP to undergo psychotherapy and established a timeline of behavioral benchmarks before he could apply for reinstatement on April 15.

Players association general counsel Tom DePaso argues the Vikings running back’s 15-game suspension — the nine games Peterson missed on paid leave, plus Minnesota’s final six games — is punishment “wildly disparate” from previous domestic violence cases.

He cannot expect a fair review without independent oversight of Goodell’s authority, which the players association argues has been tainted by negative publicity following the Ray Rice domestic abuse scandal.

Rice and Peterson have become intertwined as wayward running backs fighting for due process under the league’s toughened personal conduct policy. But there are notable differences.

On Friday, former U.S. District Judge Barbara Jones overturned the NFL’s indefinite suspension of Rice, whom Goodell initially suspended two games before video surfaced of the former Baltimore Ravens star punching out his fiancee at an Atlantic City, N.J., casino.

Jones, hired by the NFL and players association as a neutral arbitrator, ruled Goodell’s punishment was “arbitrary,” the same argument the union is using to defend Peterson.

However, Peterson’s appeal was heard by Henderson, a former NFL executive who routinely hears suspension appeals.

Peterson has become a pawn in a broader labor battle over Goodell’s ultimate authority to discipline players. The union claims the toughened policy, which calls for six-game minimum suspensions for incidents of domestic or child abuse, must be collectively bargained.

It remains unclear when Henderson will issue a ruling. The NFL has not offered a timeline. If Peterson loses, he might sue the league in federal court and petition a judge for an injunction to overturn the suspension.

Meanwhile, the Vikings have only four games remaining and have publicly supported the NFL’s suspension of their franchise player.

Peterson, 29, remains on the exempt list, drawing on his $11.75 million salary. He is signed through 2017 and due almost $40 million on his remaining contract.

However, he already has earned $36 million in guaranteed salary, and the Vikings can release him without penalty or trade him in March.

—The Associated Press contributed to this report.