class Animal
trait Furry extends Animal
trait HasLegs extends Animal
trait FourLegged extends HasLegs
class Cat extends Animal with Furry with FourLegged

The last part of the linearization of Cat is the linearization of its superclass, Animal, which is copied as-is. The second to last part is the linearization of the first mixin, trait Furry, but all classes that are already in the linearization of Animal are left out now. This is preceded by the linearization of FourLegged, where again any classes that have already been copied in the linearizations of the superclass or the first mixin are left out.