A Toronto woman who vanished five years ago was murdered -- and her remains burned -- for being the odd woman out in a love triangle, court heard Monday.

Crown attorney Jill Cameron laid out the prosecution's first-degree murder case against Dellen Millard, 32, of Toronto, and Mark Smich, 30, of Oakville, Ont., in the death of 23-year-old Laura Babcock, whose body has not been found.

Cameron walked the jury through some of the evidence the prosecution will call, including text messages between Millard and his girlfriend.

"First I'm going to hurt her, then I'll make her leave. I will remove her from our lives," Millard allegedly texted his girlfriend at the time, Christina Noudga.

The Crown alleges Millard bought an incinerator shortly before Babcock went missing in the summer of 2012 and used it in late July to burn Babcock's remains.

"I expect you'll hear Miss Babcock told Miss Noudga she was still sleeping with Mr. Millard -- and Miss Noudga was very upset about this," Cameron told the jury.

Millard and Smich have pleaded not guilty to the charges. The trial is expected to last 10 weeks.

Babcock was allegedly murdered at Millard's home on July 3 or 4, 2012, then her remains burned a few weeks later in a large incinerator, named "The Eliminator," at his farm in North Dumfries, court heard.

The Crown said Millard spent thousands of dollars on a commercial incinerator -- after a failed attempt to build a homemade one -- that was delivered the day after Babcock's last known communication with anyone.

Cameron showed the jury a video of Smich rapping.

"The b---h started off all skin and bone, now the b---h lay on some ashy stone," Smich sings in the video. "Last time I saw her she was outside the home. If you go swimming you can find her phone."

Cameron said those words were written on Babcock's iPad, which was being used by Smich, on July 23, 2012, the night the Crown says the pair put her body into an incinerator.

The Crown also showed a photograph of Smich in front of the incinerator and there was another photo of the device's door open and flames shooting out.

Clayton Babcock, the missing woman's father, was first to testify, saying he hadn't heard from his daughter since speaking with her briefly on the phone on June 30, 2012.

That same day, he said, Laura dropped off her dog, Lacey, and some money, saying she was going on a trip with a man.

He said in the months leading up to her disappearance his daughter struggled with mental health issues and was seeing a psychiatrist. She would tell friends she was diagnosed with borderline personality disorder.

She wasn't thrilled with her father's house rules, which included a midnight curfew on weeknights, and she spent time living at friends' places in the months before her disappearance, court heard.

"We still have Lacey and in a weird way, it's helped us make it through the years," Clayton Babcock said.

"Every time I see the dog I think of her and of better times."

Millard, who is representing himself, grilled Clayton Babcock about not telling the truth about life at home, and hitting his daughter, which the father denied.

The judge admonished Millard at one point for his repetitive questioning.

Shawn Lerner, Babcock's ex, was next to testify, telling court about Babcock's final days before vanishing. He had loaned her an iPad the week before she disappeared, to help with her search for an apartment.

By June, Babcock had become transient after a falling out with her family, court heard. She surfed from couch to couch with her dog before finally leaving the pet with her parents a few days before going missing.

Lerner said he searched for Babcock, talking to many of her friends and her family.

Her last eight phone calls were to Millard, Lerner told court, after reviewing her cell phone bill with her family. Lerner said he confronted Millard with the information a few weeks later at a coffee shop in Mississauga, Ont.

Millard said Babcock was addicted to drugs and she was calling him about that, Lerner said, pressing him on the nature of the calls and about a call that lasted 23 minutes.

"He seemed to imply that she's gone and that she got mixed up with the wrong type of people," Lerner told court.

Lerner told court he asked Millard if the two were sexually involved, which he said Millard vehemently denied.

Lerner said he hasn't heard from Babcock since a text from her on July 1, 2012. He filed a missing persons report with police two weeks after that text.