YES

---- CR(R)
---- R : left-linear, C : CR and CP-closing, and Cdup/R : SN
R:
+(x,0()) -> x
+(x,s(y)) -> s(+(x,y))
-(0(),x) -> 0()
-(x,0()) -> x
-(s(x),s(y)) -> -(x,y)

CP(R):
0() -> 0()
0() -> 0()

critical-pair-closing system C:


CR(C): see below.

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