I recal lthe definition
Causal Invariance: A property of multiway graphs whereby all possible
paths yield the isomorphic causal graphs. When causal invariance
exists, every branch in the multiway system must eventually merge.
Causal invariance is a core property associated with relativistic
invariance, quantum objectivity, etc. In the theory of term rewriting,
a closely related property is confluence. In a terminating system,
causal invariance implies that whatever path is taken, the "answer"
will always be the same.
Consider the rules B-> A, C -> A acting on a word composed exclusively of letters from the alphabet {A, B, C}. This system is evidently causally invariant, because all the brances will merge to the same word after the substitution of all B and all C by A.
On the other hand, the system obtained by reversing the rules A-> B, A -> C will be non-causally invariant for any word containing at least one "A". For example, applying these rules to A, we obtain two brances B and C, which cannot merge, since there is not rule to transform neither B nor C.