Arthur was jailed for 16 years with a non-parole period of 13 years in May last year.

The appeal was heard in the Court of Appeal in Melbourne on Tuesday.

The director of public prosecutions claimed the sentence was “manifestly inadequate in all the circumstances”.

Supreme Court Justice Lex Lasry handed down the original sentence.

Arthur pleaded guilty to murdering his housemate Ms Kelly on January 20, 2016. He struck her to the head with a hammer “six to seven times”, and then helped to orchestrate a cover-up of the crime.

He dumped her body in bushland off Bendigo-Maryborough Road in Shelbourne, and lead police to the body almost two weeks later when suspicion intensified.

Arthur was involved in a plan to attempt to enrol Ms Kelly’s children in kindergarten and school following the murder, and was listed as the children’s “papa”.

Judgement has been reserved and no date has been set for the court’s ruling on the appeal.