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(___y37)),___y36) -> -(___y37,___y36)
-(d(d(___y41)),___y40) -> -(___y41,s(s(___y40)))
-(___y54,___y56) -> -(s(___y54),s(___y56))
-(___y62,___y63) -> -(d(s(___y62)),___y63)
-(___y82,s(s(___y85))) -> -(d(d(___y82)),___y85)

critical-pair-closing system C:
-(0(),0()) -> 0()
-(x,s(y)) -> -(d(x),y)
d(s(x)) -> x
-(s(x),s(y)) -> -(x,y)

CR(C): see below.

---- CR(R)
---- R : linear and strongly closed [Huet, 1980]
R:
-(0(),0()) -> 0()
-(x,s(y)) -> -(d(x),y)
d(s(x)) -> x
-(s(x),s(y)) -> -(x,y)
CP(R):
-(d(s(___y113)),___y112) -> -(___y113,___y112)
-(___y126,___y127) -> -(d(s(___y126)),___y127)