At the beginning, Tim says it was a story that was rather grim. As they’re running, none of them are carrying an axe. Tim chose the tree they would climb. That’s where the axe was. The murder was planned from the start.
For the record, dogs are actually very good at adapting to amputation. Many have been found to not notice the loss until a while later - if it's been amputated under sedatives - and they continue to be just as playful and energetic.
I really like when there’s three people with three very different personalities/ scenarios. Like Tim got super serious and went to the extreme instantly pretty much because of certain things. Then there’s Jim, the one person who doesn’t want to do that extreme thing, but has no choice and can’t stop Tim. Lastly, Kim. He’s the one that gets effected the most (aka dies) and tries to get out of the situation. It’s really intriguing to see these types of scenarios happen between the characters, because it’s actually pretty mental if you think hard about it