  We prove that the depth formula holds for two finitely generated
Tor-independent modules over Cohen-Macaulay local rings if one of the modules
considered has finite reducing projective dimension (for example, if it has
finite projective dimension, or the ring is a complete intersection). This
generalizes a result of Bergh-Jorgensen which shows that the depth formula
holds for two finitely generated Tor-independent modules over Cohen-Macaulay
local rings if one of the modules considered has reducible complexity and
certain additional conditions hold.
  Each module that has reducible complexity also has finite complexity and
finite reducing projective dimension, but not necessarily vice versa. So a new
advantage we have is that, unlike modules of reducible complexity, Betti
numbers of modules of finite reducing projective dimension can grow
exponentially.
