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The two clubs have joined Inter Allies as the three teams that have been demoted to the Division One League.
Liberty drew with King Faisal on the final day of the season – a result which saw them finish 17th on the league table.
Meanwhile, Dwarfs defeated Bechem United 2-1 on Sunday, finishing on 41 points together with King Faisal and Elmina Sharks.
However, the Cape Coast-based side suffered relegation due to the superior head to head record by their rivals.
This brings a close to the 2020-21 Ghana Premier League season, with Hearts of Oak being crowned champions.
The Phobians finally laid their hands on the league trophy after Saturday’s game against WAFA in Sogakope.
The Phobians were beaten 1-0 by the Academy Boys, with Atte Youssifou’s second half strike separating the two teams.
However, the result did not matter as the club ended its 12-year wait for a major trophy, having endured a dry spell since 2009.
Asante Kotoko, WAFA and Aduana Stars complete the top four in that order.