Jozef Puska denies killing the 23-year-old while she was out for a jog in County Offaly.
Ms Murphy died along the Grand Canal Way near Tullamore on 12 January 2022.
Mr Puska, 33 and from Mucklagh in County Offaly, gave evidence at Dublin’s Central Criminal Court last week.
The jury started http://darsalas.com/ deliberating on the case on Wednesday afternoon and is due to resume on Thursday morning.