Police in the Republic of Ireland believe the young teacher brutally murdered while out for an afternoon jog was killed by a total stranger.
Ashling Murphy was killed on Wednesday afternoon along the banks of the Grand Canal at Cappincur, Co Offaly.
The 23-year-old was a a primary school teacher in the town.
Gardai vowed "no stone will be left unturned" in bringing her killer to justice. A man who was being questioned has been released after gardai said he is no longer a suspect in the murder investigation.
Superintendent Eamonn Curley said: "This area here, where the crime occurred, is popular among Tullamore residents and is widely used for recreational purposes.
"Aisling was a schoolteacher in Durrow National School. Our prayers are with Ashing's family at this time and indeed the wider community, her teaching colleagues and the children she taught who are without their teacher today.
The detective said emergency services responded to a call around 4pm and medics battled to save Ashling's life. He said her injuries were consistent with an assault.
Superintendent Eamonn Curley said: "At this stage, there is no information that the victim and her killer were known to each other.
"From our enquiries we have carried out, we believe this crime was committed by one male who acted alone."
He said gardai retain an "open mind" in the investigation and appealed to the public for assistance and asked any witnesses to come forward.
The killing has provoked widespread sorrow at the death of a "young woman, simply out for a run".
Who was Ashling Murphy?
Gardai said Ms Murphy was teacher at Durrow National School from the Blueball area of Tullamore.
The Cappincur canal area where she was attacked is popular with residents and widely used for recreational purposes."
Gardai liaisons were providing support to her family and a post mortem is being carried out, he added.
The Irish National Teachers Organisation said in a statement: "We offer our sincere condolences to the family and friends of Ashling Murphy, her colleagues and pupils at Scoil Naomh Colmcille and all who knew her.
"For such an appalling tragedy to befall a young woman, who only recently began her teaching career, adds to the profound sense of loss and grief felt."
Local TD Barry Cowen said: "Our locality like the whole country is stunned and numbed. Thoughts, prayers with her family, friends, colleagues and community."
She was 'simply out for a run'
Leaders across the island of Ireland have reacted in shock to the teacher's death.
Sinn Féin leader Mary-Lou McDonald tweeted: "Horrific. A young woman's life brutally stolen. In broad daylight. In a busy place. A nightmare for a family, friends and community."
Northern Ireland's deputy First Minister Michelle O'Neill said violence against women "must be stopped".
The whole country is "shocked and devastated," she tweeted.
"Her family, friends, colleagues and the children she taught are in our thoughts this morning."
Education Minister Simon Harris tweeted: “A young woman, simply out for a run in the afternoon and brutally killed.
“Thinking of her and her family and community tonight & their unimaginable pain.
“We must all act to end violence against women. We all have a responsibility.”
The Office of the State Pathologist and the Garda Technical Bureau have been notified, as gardai urgently appeal for any witnesses to come forward.
Gardai are eager to hear from anyone who was in the Cappincur/Canal walk area of Tullamore, County Offaly before 4pm on Wednesday.