Indeed, most serial killers and other psychopaths start by torturing animals. I don’t know about execution, but I don’t want them back in the free population. Confinement in a metal institution is appropriate.
John Douglas, essentially the founder of the FBI's ISU (profiling unit) identified a triad of serial killer behaviors:
1. animal torture/mutilation
2. arson/fire starting
3. latent bedwetting (into the teen years)
In his extensive interviews with serial killers, Douglas noted that virtually without exception, serial killers had at least two of these behaviors in their histories. Animal torture by fire scores these girls a twofer.