The jury in the John Crerar murder trial resumes its deliberations today after spending last night in a hotel.
The jury spent two hours considering a verdict yesterday after four weeks of evidence in the trial.
Former army sergeant John Crerar (54), a father-of-five of Woodside Park, Kildare, has denied the murder of Philomena Murphy (23), who was known as Phyllis, on a date unknown between December 22nd, 1979, and January 18th, 1980.
At the time of her death, Phyllis Murphy was living in digs in Rathangan, Co Kildare. Her body was found, naked and strangled, in a forested area in Co Wicklow on January 18th, 1980. The state pathologist found injuries consistent with rape.
The prosecution alleges DNA from samples extracted from the body of Phyllis Murphy matched DNA from blood samples given by John Crerar. The prosecution also called former co-workers of John Crerar, who alleged he did not turn up for work at the times he said he did on the night Phyllis Murphy disappeared.
The defence argues that the jury should disregard the changed evidence of the former co-workers as unreliable.
The defence also argues that the risk of a mistake or of a chance match of DNA occurring was too high for the jury to convict Mr Crerar on the DNA evidence alone.
In his address yesterday, Mr Justice Liam McKechnie told the jury it must resolve the "major conflict of evidence" between John Crerar and his former co-worker, Paddy Bolger.
He also reminded them of the evidence of Dr Maureen Smyth of the State Forensic Science Laboratory on DNA analysis that she carried out on blood samples taken from Mr Crerar and samples taken from the body of the deceased.
Dr Smyth said the estimated chance of somebody unrelated to Mr Crerar in the general population having the same profile was one in 1,000 million.
"If you accept the DNA evidence, you must still go on and consider whether the prosecution has proved beyond a reasonable doubt that the accused person murdered Phyllis Murphy", Mr Justice McKechnie told the jury.
Earlier, in his closing speech, defence lawyer Mr Roger Sweetman SC argued that the risk of a chance match or a mistake in the DNA evidence against the accused man was too high to rely on it to convict him of murder.
He argued the other prosecution evidence against his client was "inconsistent" and had "huge gaps".
But the prosecution counsel, Mr Michael Durack SC, said the jury should consider the evidence of Dr Smyth that DNA analysis was internationally recognised.
He also asked the jury what Paddy Bolger and two other former co-workers of Mr Crerar had to gain from giving a false account of his movements on the night of December 22nd.
The jury resumes its deliberations today.