  We introduce LAM, a subsystem of IMALL2 with restricted additive rules able
to manage duplication linearly, called linear additive rules. LAM is presented
as the type assignment system for a calculus endowed with copy constructors,
which deal with substitution in a linear fashion. As opposed to the standard
additive rules, the linear additive rules do not affect the complexity of term
reduction: typable terms of LAM enjoy linear strong normalization. Moreover, a
mildly weakened version of cut-elimination for this system is proven which
takes a cubic number of steps. Finally, we define a sound translation from
proofs of LAM into linear lambda terms of IMLL2, and we study its complexity.
