MIAMI BEACH — Monday brings their journey’s end, and Jason Taylor knows it. Just last week he did a Google search of his prized students, Rueben Bain Jr. and Akheem Mesidor, to remember how it started and measure how far they’d come.

“I found a picture of Rueben with no facial hair — now he’s full-bearded,’’ said Taylor, the University of Miami’s defensive line coach and Miami Dolphins Hall of Famer. “Mess came here with these frosted tips in his dreadlocks. He shaved them off.”

Miami’s championship game against Indiana at Hard Rock Stadium ends this season where the primary key for the Hurricanes once again will be the ability of Bain and Mesidor to pressure the opposing quarterback, this time Indiana star Fernando Mendoza.

But this game also ends one of the more compelling teams within a Miami team. You don’t know who’s been more fortunate in this coaching/players relationship: Taylor, for getting to work with two top talents who will be high NFL draft picks; or Bain and Mesidor for learning from a Hall of Fame talent with a matching personality to help them succeed to the NFL.

Each day for the past couple of seasons, Bain and Mesidor would sit in Taylor’s office and “talk everything but football,’’ as Mesidor said.

“Politics, news, Canada (Mesidor is Canadian) — whatever comes up,” Taylor said Saturday at the championship game’s media day at the Miami Beach Convention Center.

By now they put their relationship with Taylor in family terms of, “like father-son,’’ as Bain says or, “older brother to younger brother,’’ Mesidor says.

“They’re like extra sons to me,’’ Taylor said.

Taylor helped recruit Bain in his opening steps as a college coach four years ago. Bain grew up in Miami and knew Taylor’s NFL fame, unlike Mesidor who grew up in Ottawa and didn’t follow football much as a youth.

“Everybody told me he was a Hall of Famer when I got here,’’ Mesidor said. “So, I did the research myself and, yeah, he was awesome.’’

That was Taylor, the havoc-raising edge rusher and commanding locker-room presence. That player never saw this next chapter coming. He coached his sons, Mason and Isaiah, in youth leagues and high school. That led to his taking a job when Mario Cristobal arrived at Miami.

“I used to laugh at the coaches after we’d fly back from a night game and finally get to the facility, and I’d leave in my car and go home for two days and they’d go upstairs to watch film,’’ Taylor said. “I’d say, ‘You guys are idiots.’ Now, I’m the guy who goes in the office.‘’

Now, he also borrows ideas from his coaches like Jimmy Johnson, Dave Wannstedt, Nick Saban and Tony Sparano.

“You take all the lessons, some of the stuff you heard them say — sometimes you thought was coachspeak,’’ he said. “I use those same tricks now and sometimes think, ‘I can’t believe I’m doing this.’‘’

Look at the results. Bain and Mesidor led Miami to 12 sacks in the playoff games against Texas A&M and Ohio State. The numbers weren’t there against Mississippi, but that’s only because Ole Miss altered its offense, as Bain said.

Taylor saw all types of players across his career. Mesidor is the football thinker, the guy who wants to not just understand his role but have backup plans for any variable. Taylor says how at times in meetings he’ll have to say the offense would never do that fourth or fifth idea Mesidor brings up while Bain will sit there and “just shake his head over the rabbit hole we’ve gone down.’’

Here’s their common ground to greatness: “I’ve never been around two guys at this age who work harder than Bain and Mess,’’ Taylor said. “It’s crazy. It’s to the point we had to pull them back to work less. We butted heads at times on that, making them get off the practice field.

“I’m trying to get them to game day and save their legs. They want to practice more. We’re literally, not coming to blows, but tears were shed. That’s how much it matters to them.”

So, now comes their last game. Farewells sometimes have a moment of their own. Taylor’s final game came in this same stadium back when it was called Sun Life Stadium on Jan 1, 2012. A defensive stand closed out the Dolphins’ tight win against the New York Jets. Taylor was then carried around the field by teammates.

If Bain and Mesidor are carried off, it’s because of a title for Miami. Monday is more a graduation for them than an end, though. The NFL awaits them. Taylor watched them grow like a proud football papa. Now the former star says as his students approach the biggest game of their career, “It’s their time.”