After having a closer look into all aspects discussed in the WP page, I'm afraid that my intuition wasn't too bad and "Monotonicity" is indeed not a good idea.

Basically because it defines for all elements x ≤ y => f(x) ≤ f(y)

Since the OP is only testing adjacent elements, this can only be true with a transitive relation inside the testing block.

But this can't be guaranteed because the user is free to apply any code there.