Question: Are both Limp Bizkit and Third Eye Blind rock bands?

Context paragraphs:
Red Star (EP): Red Star is a digital-only EP by Third Eye Blind released in 2008 in anticipation of their fourth studio album "Ursa Major".  Previews of the songs on the EP were posted to the band's myspace page on November 12, 2008, and it was released officially on November 18, 2008 through all major digital music outlets.  Also released with the EP was a music video for "Non-Dairy Creamer" featuring Third Eye Blind's recent Japan tour.

Third Eye Blind: Third Eye Blind is an American rock band formed in San Francisco in 1993.  The songwriting duo of Stephan Jenkins and Kevin Cadogan signed the band's first major label recording contract with Elektra Records in 1996, which was later reported as the largest publishing deal ever for an unsigned artist.  The band released their self-titled album, "Third Eye Blind", in 1997, with the band largely consisting of Jenkins (lead vocals, rhythm guitar), Cadogan (lead guitar), Arion Salazar (bass guitar), and Brad Hargreaves (drums).  Shortly after the release of the band's second album in 1999, "Blue", with the same line-up, Cadogan was released from the band under controversial circumstances.

Home Sweet Home/Bittersweet Symphony: "Home Sweet Home / Bittersweet Symphony", also known as "Bittersweet Home" is a song by American rock group Limp Bizkit.  It was released in December 2005 as the only single from the compilation album "Greatest Hitz".  The song is a medley of "Home Sweet Home" by Mötley Crüe and "Bitter Sweet Symphony" by The Verve.  It is, along with the songs "Why" and "Lean On Me", the only new content on the "Greatest Hitz" compilation, and is the third cover song Limp Bizkit has released on an album (the others being The Who's "Behind Blue Eyes", and George Michael's "Faith").

Out of the Vein: Out of the Vein is the third studio album by American rock band Third Eye Blind.  Released on May 13, 2003, "Out of the Vein" is the band's first album with guitarist Tony Fredianelli, who replaced longtime guitarist Kevin Cadogan in 2000.  It would also be Third Eye Blind's final album with Elektra Records.

Kevin Cadogan: Kevin Rene Cadogan (born August 14, 1970) is an American singer/songwriter, producer and rock guitarist.  A founding member of the band Third Eye Blind, he performed with the band from 1993 to 2000.  He co-wrote some of Third Eye Blind's most notable hits, including "How's It Going to Be", "Losing a Whole Year", and "Graduate", and 10 of the 14 songs on their debut album "Third Eye Blind".

Stephan Jenkins: Stephan Douglas Jenkins (born September 27, 1964) is an American musician best known as the lead singer, songwriter, and guitarist for Third Eye Blind.  Under Jenkins's leadership, Third Eye Blind has sold over 12 million copies worldwide of five albums: "Third Eye Blind" (1997), "Blue" (1999), "Out of the Vein" (2003), "Ursa Major" (2009), and "Dopamine" (2015).  Jenkins wrote or co-wrote all of the band's most notable hits, including "Semi-Charmed Life", "Jumper", "How's It Going to Be", "Losing a Whole Year", "Graduate", "Deep Inside of You", "Never Let You Go" and "Blinded".

Third Eye Blind (album): Third Eye Blind is the debut studio album by American rock band Third Eye Blind, released on April 8, 1997.  The album spawned five singles, including the top ten chart hits "Semi-Charmed Life", "Jumper", and "How's It Going to Be".

Limp Bizkit: Limp Bizkit is an American rap rock band from Jacksonville, Florida, formed in 1994.  Their lineup consists of Fred Durst (lead vocals), Sam Rivers (bass, backing vocals), John Otto (drums, percussion), and Wes Borland (guitars, backing vocals).  Their music is marked by Durst's angry vocal delivery and Borland's sonic experimentation.  Borland's elaborate visual appearance, which includes face and body paint, masks and uniforms, also plays a large role in the band's elaborate live shows.  The band has been nominated for three Grammy Awards, have sold 40 million records worldwide and won several other awards.

Blue (Third Eye Blind album): Blue is the second studio album by American rock band Third Eye Blind, released on November 23, 1999.  The album's creation was difficult, namely due to power struggles and arguments between frontman Stephan Jenkins and lead guitarist Kevin Cadogan, leading to a quick but isolated recording experience between members.  The album was generally well received by critics, and was certified platinum by the RIAA, but performed below the band's prior album, the multi-platinum "Third Eye Blind".  While managing to stay together for the creation of the album, shortly after its release, the band fired Cadogan, touring in support of the album with replacement guitarist Tony Fredianelli.  As such, the album was the last to feature Cadogan, and the last to be released without significant gaps and delays prior to release.

Counterfeit (song): "Counterfeit" is a song by the American nu metal band Limp Bizkit from their debut album "Three Dollar Bill, Y'all" (1997).  Notable for showcasing guitarist Wes Borland's experimental playing style, the song was written by Borland, DJ Lethal, Fred Durst, John Otto and Sam Rivers as a response to local bands that copied Limp Bizkit's style.

Supporting paragraphs: Limp Bizkit Third Eye Blind
Answer: yes