YES

---- CR(R)
---- R : left-linear, C : CR and CP-closing, and Cdup/R : SN
R:
-(+(x,y)) -> +(-(x),-(y))
+(-(x),-(y)) -> -(+(x,y))

CP(R):
+(+(-(___y21),-(___y22)),-(___y24)) -> -(+(+(___y21,___y22),___y24))
+(-(___y23),+(-(___y21),-(___y22))) -> -(+(___y23,+(___y21,___y22)))
-(-(+(___y25,___y26))) -> +(-(-(___y25)),-(-(___y26)))

critical-pair-closing system C:
-(+(x,y)) -> +(-(x),-(y))

CR(C): see below.

---- CR(R)
---- R : left-linear, C : CR and CP-closing, and Cdup/R : SN
R:
-(+(x,y)) -> +(-(x),-(y))

CP(R):


critical-pair-closing system C:


CR(C): see below.

---- CR(R)
---- R is empty.