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):
+(+(-(___y5),-(___y6)),-(___y8)) -> -(+(+(___y5,___y6),___y8))
+(-(___y7),+(-(___y5),-(___y6))) -> -(+(___y7,+(___y5,___y6)))
-(-(+(___y9,___y10))) -> +(-(-(___y9)),-(-(___y10)))

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

CR(C): see below.

---- CR(R)
---- R : linear and strongly closed [Huet, 1980]
R:
-(+(x,y)) -> +(-(x),-(y))
CP(R):