  Our method of density elimination is generalized to the non-commutative
substructural logic GpsUL*. Then the standard completeness of GpsUL* follows as
a lemma by virtue of previous work by Metcalfe and Montagna. This result shows
that GpsUL* is the logic of pseudo-uninorms and their residua and answered the
question posed by Prof. Metcalfe, Olivetti, Gabbay and Tsinakis.
