Question: What song did the performer of Imagine write for David Bowie?

full_context: Document 1: Imagine (John Lennon song): ``Imagine ''is a song written and performed by English musician John Lennon. The best - selling single of his solo career, its lyrics encourage the listener to imagine a world at peace without the barriers of borders or the divisions of religion and nationality and to consider the possibility that the whole of humanity would live unattached to material possessions.
Document 2: Fame (The Game): "Fame (The Game)" was the second official single from Donna Summer's 2008 studio album "Crayons". It reached #1 on the "Billboard" Hot Dance Club Play chart.
Document 3: I'm Afraid of Americans: "I'm Afraid of Americans" is a single by David Bowie from the 1997 album "Earthling". The song, co-written by Bowie and Brian Eno, was originally written during Bowie's studio sessions for the 1995 album "Outside" but was not released until a rough mix appeared on the soundtrack to the film "Showgirls", and was subsequently remade for "Earthling". A top 20 hit in Canada, the rework also peaked at number 66 on the "Billboard" Hot 100 and spent 16 weeks on that chart. This was the final Bowie single which charted on the Hot 100 until "Blackstar" and "Lazarus" following his death.
Document 4: Early 1970: "Early 1970" is a song by English musician Ringo Starr, released in April 1971 as the B-side to his hit single "It Don't Come Easy". It was inspired by the break-up of the Beatles and documents Starr's relationship with his former bandmates, John Lennon, Paul McCartney and George Harrison. The lyrics to the verses comment in turn on each of the ex-Beatles' personal lives and the likelihood of each of them making music with Starr again; in the final verse, Starr acknowledges his musical limitations before expressing the hope that all the former Beatles will play together in the future. Commentators have variously described "Early 1970" as "a rough draft of a peace treaty" and "a disarming open letter" from Starr to Lennon, McCartney and Harrison.
Document 5: "Heroes" (David Bowie song): ``'Heroes' ''is a song recorded by the English musician David Bowie, written by Brian Eno and Bowie. Produced by Bowie and Tony Visconti, it was recorded in July and August 1977, and released on 23 September 1977. A product of Bowie's`` Berlin'' period, the track was not a huge hit in the UK or US at the time, but has gone on to become one of Bowie's signature songs. In January 2016, following Bowie's death, the song reached a new peak of number 12 in the UK Singles Chart. ``'Heroes' ''has been cited as Bowie's second-most covered song after`` Rebel Rebel''.
Document 6: "Heroes" (David Bowie song): ``'Heroes' ''is a song recorded by the English musician David Bowie, written by Brian Eno and Bowie. Produced by Bowie and Tony Visconti, it was recorded in July and August 1977, and released on 23 September 1977. A product of Bowie's`` Berlin'' period, the track was not a huge hit in the United Kingdom or United States at the time, but has gone on to become one of Bowie's signature songs. In January 2016, following Bowie's death, the song reached a new peak of number 12 in the UK Singles Chart. ``'Heroes' ''has been cited as Bowie's second-most covered song after`` Rebel Rebel''.
Document 7: Imagine (1972 film): Imagine is a 1972 television film by John Lennon and Yoko Ono, filmed mostly at their Tittenhurst Park home in Ascot, England, during 1971, and intended for television. All the songs from Lennon's "Imagine" album appear in the soundtrack, and also the songs "Mrs. Lennon" and "Don't Count the Waves", from Ono's album "Fly".
Document 8: Ram (album): Ram (stylised as RAM) is a studio album by Paul McCartney and Linda McCartney, released in May 1971 on Apple Records. "Ram" was recorded amid McCartney's legal action in the United Kingdom's High Court to dissolve the Beatles' partnership, following the band's break-up the year before. It was recorded in New York with guitarists David Spinozza and Hugh McCracken, and future Wings drummer Denny Seiwell. Its release coincided with a period of bitter acrimony between McCartney and his former bandmate John Lennon, who perceived verbal slights in the lyrics to songs such as "Too Many People".
Document 9: Mr. Tambourine Man: The song has been performed and recorded by many artists, including the Byrds, Judy Collins, Melanie, Odetta, and Stevie Wonder among others. The Byrds version was released in April of 1965 as their first single on Columbia Records, reaching number 1 on both the "Billboard" Hot 100 chart and the UK Singles Chart, as well as being the title track of their debut album, "Mr. Tambourine Man." The Byrds' recording of the song was influential in popularizing the musical subgenres of folk rock and jangle pop, leading many contemporary bands to mimic its fusion of jangly guitars and intellectual lyrics in the wake of the single's success.
Document 10: Jealous Guy: ``Jealous Guy ''is a song by English rock musician John Lennon from his 1971 album Imagine. Lennon began writing the song in 1968, when, as`` Child of Nature'', it was among the many songs demoed by the Beatles before they recorded their self - titled double album (also known as the ``White Album ''). The lyrics were originally inspired by a lecture given by Maharishi Mahesh Yogi in early 1968, when the Beatles attended his spiritual retreat in Rishikesh, India. In its rewritten form, the song serves as a confessional in which Lennon addresses the feelings of inadequacy that resulted in his failings as a lover and husband.
Document 11: I Found Out: "I Found Out" is a song by the English musician John Lennon from his 1970 album "John Lennon/Plastic Ono Band".
Document 12: God (John Lennon song): "God" is a song from John Lennon's first post-Beatles solo album, "John Lennon/Plastic Ono Band". The album was released on 11 December 1970 in the United States and the United Kingdom.
Document 13: David Bowie: Dissatisfied with his stage name as Davy (and Davie) Jones, which in the mid-1960s invited confusion with Davy Jones of The Monkees, Bowie renamed himself after the 19th - century American pioneer James Bowie and the knife he had popularised. His April 1967 solo single, ``The Laughing Gnome '', using speeded - up thus high - pitched vocals, failed to chart. Released six weeks later, his album debut, David Bowie, an amalgam of pop, psychedelia, and music hall, met the same fate. It was his last release for two years.
Document 14: Imagine (John Lennon album): Imagine is the second studio album by John Lennon after his departure from the Beatles. Recorded and released in 1971, the album's musical arrangements are more elaborate compared to the basic, small-group arrangements of his first album, "John Lennon/Plastic Ono Band".
Document 15: Fame (David Bowie song): ``Fame ''is a song recorded by David Bowie, initially released in 1975. Written by Bowie, Carlos Alomar and John Lennon, it was a hit in North America, becoming Bowie's first number 1 single in the Canadian Singles Chart as well as the U.S. Billboard Hot 100. The song was one of the more successful singles of the year, ranking at number 7 on the Billboard Year - End Hot 100. It was less successful in Europe, reaching number 17 in the UK Singles Chart.
ground_truth: ``Fame ''
sub_queries: Imagine >> performer Answer: John Lennon
what song did John Lennon write for david bowie Answer: ``Fame ''