YES

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

CP(R):
-(d(s(___y1189)),___y1188) -> -(___y1189,___y1188)
-(d(d(___y1193)),___y1192) -> -(___y1193,s(s(___y1192)))
-(___y1206,___y1208) -> -(s(___y1206),s(___y1208))
-(___y1214,___y1215) -> -(d(s(___y1214)),___y1215)
-(___y1234,s(s(___y1237))) -> -(d(d(___y1234)),___y1237)

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

CR(C): see below.

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

CP(R):


critical-pair-closing system C:


CR(C): see below.

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