A historic High Court trial featuring a businessman and Google bosses should end next week.
The man was convicted of "conspiracy to account falsely" in the 1990s and wants Google to stop linking his name to internet media reports about the offence.
He says the conviction is legally "spent" and says he has a "right to be forgotten".
Google bosses dispute his claims.
Mr Justice Warby began analysing evidence at a High Court trial in London on Tuesday.
The hearing has been adjourned.
It is due to resume on Tuesday and conclude on Wednesday.
Lawyers say it is the first time such a "right to be forgotten" claim has been tried in England.
The judge has barred journalists from identifying the man in reports of the case.