Logic pointed to nothing other than a Wales win - but logic does not often apply to Wales at the World Cup.

Their hearts had been broken too many times to be overly confident, even if form, world ranking and all other measurable factors suggested they would beat France comfortably.

History's pain kept Welsh complacency at bay, the most agonising episode of all being the 2011 semi-final loss to France.

Despite having to play almost an entire match with 14 men because of Sam Warburton's red card, Wales still could have won, and to lose by a single point only deepened their grief in New Zealand.

Eight years on in Japan, they exorcised those demons with a near mirror image of events in Auckland.

This time it was France who saw red - Sebastien Vahaamahina inexplicably elbowing Aaron Wainwright - and now it was Les Bleus who had to suffer the anguish of a one-point defeat.

Captain Alun Wyn Jones and George North were the only Wales players to play in both matches, while Maxime Medard was France's sole survivor.

But despite the changes in personnel, Wales head coach Warren Gatland said in the build-up to this rematch that his players were using the hurt of 2011 as a source of inspiration.

"I think for the players and coaches that were involved in 2011, that is an advantage in terms of preparation and remembering about that," he said afterwards.

"It is ironic the last time we were in a World Cup there was a red card and it was a one-point game as well.

"We did not play our best but we showed some character, and that is testament to this group of men - we can be excited about looking forward to a semi-final."

Gatland avoids an early end to his reign

That excitement is justified. For all the pre-tournament talk of this being Wales' best chance yet to win a first World Cup, this will only be their third semi-final.

Wales lost the other two - in 1987 and 2011 - so they will savour next Sunday's meeting with South Africa, and nobody more so than Gatland.

The New Zealander will step down as head coach at the end of this World Cup and, for 75 minutes in Oita, it looked like his glittering 12-year reign would come to an early and ignominious end.

"You start going through a lot of different emotions," Gatland said, admitting that he thought this might be it.

"What I am going to be saying in here [to the media at his post-match conference], what I am going to be saying on the television - you are thinking on those potential scenarios.

"France played exceptionally well and they have made a lot of progress over the last five months.

"I definitely went through a lot of emotions today but coming in at half-time and getting some clear messages to the players about what we were going to do in the second half [was important].

"I am proud of the players and how we hung in there."

Those players were not going to allow Gatland - arguably Wales' greatest coach - to leave on such a flat note.

Having trailed 12-0 early on, Wales were 19-10 down at half-time but, despite continuing to play poorly by their own recent high standards, they found a way to win.

This is what Wales do under Gatland.

They were 16-0 down away against France at half-time in their opening Six Nations fixture in February, and yet they fought back to win 24-19 and set the ball rolling for a third Grand Slam of the Gatland era.

In Paris that evening, Gatland said his team had "forgotten how to lose".

That fortitude was evident in another comeback victory during that campaign at home to England, and it has been there for the world to see in Japan as Wales withstood a fierce Australian revival in Tokyo and then overcame an explosive start from Fiji to prevail in Oita.

They had to delve into that deep well of resolve once more upon their return to Oita to face France.

Wales were not once in the lead until Dan Biggar's match-winning conversion from Ross Moriarty's try in the 75th minute, itself a play within a play, a tale of redemption for Moriarty, whose first-half sin-binning had cost his side seven points.

Even if their form had deserted them, Wales never lacked belief.

They stuck to their task unerringly. Although France had not played for two weeks, they were tiring after Vahaamahina's red card.

By contrast, Wales, who pride themselves on being one of the fittest teams in the world, seemed to get stronger as time wore on.

"We've prepared for this. We've been to some dark places in the preparation for these moments and games," captain Alun Wyn Jones said.

"The weeks and days do feel a little bit longer obviously because of the magnitude of the occasion coming up.

"Physically, this is what we've prepared for and we're ready to go for the next one."

A World Cup a decade in the making

Wales have been planning for this World Cup for years, and those preparations have been particularly focused over the past 18 months.

Last year's summer tour of the United States and Argentina helped build strength in depth, with debuts for players such as Wainwright, man of the match against France and now a first-team regular.

Then there was the clean sweep of last autumn's Tests - including victories over Australia and South Africa - and this year's Six Nations Grand Slam, all of which contributed to a record winning run of 14 matches.

Wales' players then started convening for World Cup training as far back as May, before embarking on gruelling training camps at altitude in the Swiss Alps and then in the searing heat of Turkey.

The planning has been meticulous, a World Cup years in the making.

When Jones was asked about the extent of Welsh preparations, he said Gatland had probably been mapping out this campaign for the past 10 years.

Now that decade boils down to two matches: a semi-final followed by what everyone involved hopes will be a final, rather than a third-place play-off.

"We're excited about being where we are. We're in a semi-final of a World Cup," Gatland said.

"Alun Wyn has been saying that we have 240 minutes to do something you'll remember for the rest of your life.

"We're down to 160 now, if you can't get excited about that, nothing will excite you."