A court will decide on Monday if Australians Myuran Sukumaran and Andrew Chan will be allowed to challenge the presidential decision to deny them clemency.
The pair's lawyers have resorted to the state administrative court in a bid to spare them from the firing squad for the 2005 Bali Nine heroin smuggling attempt.
The court in February threw out their challenge, determining it didn't have the authority to examine the decrees by President Joko Widodo.
It's now considering the appeal and will hand down its decision on Monday.
Wrapping up their arguments on Wednesday, lawyer for Chan and Sukumaran, Leonard Arpan, said the administrative court had the authority to examine a clemency decision.
"Clemency in the form of a presidential decree falls within state administrative matters," he told the court.
"The state administrative court is the forum to challenge it."
Outside court, Mr Arpan told reporters they had done their best to fight for the Australians, who await execution on Nusakambangan island.
"I don't want to go too far in assessing the conclusion from the state, for the sake of respecting the judges in making all considerations before giving a decision in this case," he said.
"Let's just respect the ongoing process.
"We did our best and we will wait for the result."
In its summary, lawyers for the state argued clemency was a matter of presidential prerogative, not open for examination in the administrative court.
"In giving clemency the president has the right to accept and reject it, based on Supreme Court opinion, but then the president doesn't have to follow that opinion," lawyer Elhari said.
"Clemency is a political authority which makes it not under the state administrative jurisdiction."
Chief judge Ujang Abdullah said the judges would carefully examine the arguments and "cannot be rushed".
The appeal has received evidence from legal experts for both sides.
Indonesia's Attorney-General HM Prasetyo is waiting for several of 10 death row drug offenders to use their remaining legal appeals before setting a date for their simultaneous execution on Nusakambanagan.
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