  Zeckendorf's theorem states that every positive integer can be written
uniquely as the sum of non-consecutive shifted Fibonacci numbers $\{F_n\}$,
where we take $F_1=1$ and $F_2=2$. This has been generalized for any Positive
Linear Recurrence Sequence (PLRS), which informally is a sequence satisfying a
homogeneous linear recurrence with a positive leading coefficient and
non-negative integer coefficients. In this and the preceding paper we provide
two approaches to investigate linear recurrences with leading coefficient zero,
followed by non-negative integer coefficients, with differences between indices
relatively prime (abbreviated ZLRR), via two different approaches. The first
approach involves generalizing the definition of a legal decomposition for a
PLRS found in Kolo\u{g}lu, Kopp, Miller and Wang. We prove that every positive
integer $N$ has a legal decomposition for any ZLRR using the greedy algorithm.
We also show that a specific family of ZLRRs lost uniqueness of decompositions.
The second approach converts a ZLRR to a PLRR that has the same growth rate. We
develop the Zeroing Algorithm, a powerful helper tool for analyzing the
behavior of linear recurrence sequences. We use it to prove a very general
result that guarantees the possibility of conversion between certain
recurrences, and develop a method to quickly determine whether a sequence
diverges to $+\infty$ or $-\infty$, given any real initial values. This paper
investigates the second approach.
