A.J. Styles

Context: On March 14, Styles returned to International Wrestling Cartel (IWC) and successfully challenged IWC Super Indy Champion Super Hentai for the title. On April 13, Styles defended the title in a rematch against Hentai, but the match ended in a no contest, meaning Styles retained the title. On May 10, Styles vacated the title. On August 23, Styles unsuccessfully challenged new Super Indy Champion Colt Cabana after the match ended at a twenty-minute time limit draw, meaning Cabana retained the title. On December 12 at IWC: Call to Arms, Styles would once again challenge Cabana for the title, but again was unsuccessful. On April 12, Styles debuted in Combat Zone Wrestling (CZW), competing at the promotions 3rd Best of the Best event. Styles teamed with Jason Cross to face Jay Briscoe and Jimmy Rave, in a losing effort. On July 20, at CZW: Deja Vu II, Styles successfully defended the NWA World Heavyweight Championship against Rave.  On September 12, Styles debuted in Maximum Pro Wrestling (MXPW), successfully challenging MXPW Television Champion Chris Sabin and Christopher Daniels in a three-way match for the title. On October 4, Styles debuted in Pro Wrestling Guerrilla (PWG), unsuccessfully challenging PWG Champion Frankie Kazarian and Christopher Daniels for the title. On November 7, Styles returned to IWA: Mid-South to take part in the promotions annual Ted Petty Invitational, which saw Styles defeating Todd Sexton is his first round match. The following night, he defeated Jerry Lynn in the quarter-finals, but later that night would be eliminated by Danny Daniels in the semi-finals. On March 20, 2004, Styles returned to IWC, entering the promotions Super Indy Survivor Showdown tournament. Styles' first match in the tournament was in the semi-finals due to unknown reasons, in which he defeated CM Punk. Later that night, Styles faced IWC Super Indy Champion Colt Cabana in the final in a winning effort, capturing the title. On April 17, Styles successfully defended the title against Homicide, and on May 8 he did so again against Christopher Daniels.  On September 17, Styles returned to IWA: Mid-South, entering the promotions 2004 Ted Petty Invitational. Styles defeated Jimmy Rave in his first round match. The following night, Styles defeated Matt Sydal in the quarter finals. Later that night, Styles defeated Arik Cannon in the semi-finals, as well as defeating Bryan Danielson and Samoa Joe in the final to win the 2004 Ted Petty Invitational. On October 21, Styles won the vacant IWA: Mid-South Heavyweight Championship, defeating Chris Sabin, Christopher Daniels and Petey Williams in a four-way dance match. Two days later on October 23, Styles lost the title to CM Punk.  On April 1, 2005, Styles returned to PWG, defeating Samoa Joe in a PWG Championship number one contender match at the promotion's All-Star Weekend - Day 1. The following night on Day 2 of All-Star Weekend, Styles successfully challenged Super Dragon for the title. Styles defended the title until August 6 at Zombies Shouldn't Run, where he lost it to Kevin Steen. On September 3, Styles entered the 2005 Battle of Los Angeles tournament, but was defeated in the finals by Chris Bosh. CANNOTANSWER

Question: Did AJ Styles have a major rivalry with Rave during 2003-2005?
Answer: Styles teamed with Jason Cross to face Jay Briscoe and Jimmy Rave, in a losing effort.