YES

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

CP(R):
-(+(___y10,___y9)) -> +(-(___y9),-(___y10))

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

CR(C): see below.

---- CR(R)
---- R : linear and strongly closed [Huet, 1980]
R:
-(+(x,y)) -> +(-(x),-(y))
+(x,y) -> +(y,x)
CP(R):
-(+(___y26,___y25)) -> +(-(___y25),-(___y26))