soundtrack - Is "The Merry-Go-Round of Life" from Howl's Moving Castle a song in the public domain?

The music was composed for the film by Joe Hisaishi (professional name of Mamoru Fujisawa), who was born in 1950. From wikipedia:

Another Miyazaki film, Howl's Moving Castle, for which Hisaishi
composed the score, was released on November 20, 2004 in Japan.

Here he is performing it himself. Very moving.