If we're going to split hairs like that then blood cells and the neurons of some species of adult fairy wasps are not alive.

And if you response is that the rest of the organism fulfills the self replication process through sexual reproduction, then why can't these cells being assisted by an outside process like the splitting chip be considered alive in whole like an animal is?

> blood cells and the neurons of some species of adult fairy wasps are not alive

That's right, they aren't. You hair and fingernails aren't alive either. Nor is your clothing despite the fact that that too is part of the human phenotype. [1]

> why can't these cells being assisted by an outside process like the splitting chip be considered alive in whole like an animal is?

Because the splitting chip isn't produced by the cells, it's produced by humans. Take the humans away and the whole process comes to a grinding halt.

[1] https://en.wikipedia.org/wiki/The_Extended_Phenotype