Is my Diffy game degenerate? Recently I posted a question about Diffy games which has gone unanswered.  Thats fine, the question is really hard, but I would like to make an easier question about Diffy games so that we can get the ball rolling.



How Diffy works

Copied from Find Diffy Games

The Diffy game works like as follows:  You start with a list of non-negative integers, in this example we will use

3 4 5 8


Then you take the absolute difference between adjacent numbers

 (8)  3   4   5   8
    5   1   1   3


Then you repeat.  You repeat until you realize you have entered a loop. And then generally the game starts from the beginning again.

3 4 5 8
5 1 1 3
2 4 0 2
0 2 4 2
2 2 2 2
0 0 0 0
0 0 0 0


Most games end in a string of all zeros, which is considered to be a lose state, but a rare few games get stuck in larger loops.



Task

Given the starting state of a Diffy game determine whether or not the game eventually reaches a state of all zeros.  You should output a Truthy or Falsy value for each of the two states.  Which corresponds to which does not matter.

The goal is to minimize the number of bytes in your source.
Pyth, 6 bytes

suaV+e


Test suite

This program is very suave. 0 (falsy) means all zeroes, anything else (truthy) means not all zeroes.

How it works:

suaV+e
suaV+eGGGQ    Variable introduction.
 u       Q    Apply the following function repeatedly to its previous result,
              starting with the input. Stop when a value occurs which has
              occurred before.
  aV          Take the absolute differences between elements at the same indices of
        G     The previous list and
    +eGG      The previous list with its last element prepended.
s             The repeated value is returned. Sum its entries. This is zero (falsy)
              if and only if the entries are all zero.