System
is an extension of multiplicative linear logic (
) with the rules
mix,
nullary mix, and a self-dual, noncommutative logical operator, called
seq. While the rules
mix and
nullary mix extend the deductive system, the operator seq extends the language of
. Due to the operator seq, system
extends the applications of
to those where the sequential composition is crucial, e.g., concurrency theory. System
is an extension of
with the rules
mix and
nullary mix. In this paper, by relying on the fact that system
is a conservative extension of system
, I show that system
is NP-complete by encoding the 3-Partition problem in
. I provide a simple completeness proof of this encoding by resorting to a novel proof theoretical method for reducing nondeterminism in proof search, which is also of independent interest.