There is no maximum length.  If you start with 0 100000 45631 16071, you won't reach 0 0 0 0 until row 24.  If you start with 0 1000000000000000000000000000 456310987307923638429144029 160713244785838867448147434, the list continues 104 rows after the initial row.  This page does not allow for irrational numbers, but if it did, we could generate an infinite list.

let a = 3 * squareroot(33)
let b = cuberoot(17 + a)
let c = cuberoot(19 + a)
let x = (-b + 2/b + 4) / 3
let y = (-c - 4/c + 5) / 3

The four numbers 0 1 x y generate an infinite list.