Class two cellular automata
Class two cellular automata, according to the classification system of Stephen Wolfram, are those where the development of all patterns tends toward simple stationary ash — either constellations of separate still lifes and oscillators, or larger regions of stable and oscillating cells.
A simple condition for considering a Life-like cellular automaton to be either class two or class one is the absense of birth conditions capable of extending the pattern's bounding box: B0, B1, B2 or B3. Beyond this, positively identifying a rule as class two is mostly not an exact science.
The Vote rule (B45678/S5678) is one of the better known provably class two cellular automata.