YES

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

CP(R):
s(___y17) -> s(___y17)

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

CR(C): see below.

---- CR(R)
---- R : linear and strongly closed [Huet, 1980]
R:
+(0(),y) -> y
s(s(x)) -> x
CP(R):
s(___y25) -> s(___y25)