YES

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

CP(R):
0() -> 0()
___y8 -> max(0(),___y8)
0() -> 0()
___y18 -> max(___y18,0())
s(max(___y32,___y31)) -> max(s(___y32),s(___y31))
max(0(),___y35) -> ___y35
max(___y39,0()) -> ___y39
max(s(___y44),s(___y43)) -> s(max(___y44,___y43))

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

CR(C): see below.

---- CR(R)
---- R : linear and strongly closed [Huet, 1980]
R:
max(x,0()) -> x
max(0(),y) -> y
max(s(x),s(y)) -> s(max(y,x))
max(x,y) -> max(y,x)
CP(R):
0() -> 0()
___y86 -> max(0(),___y86)
0() -> 0()
___y96 -> max(___y96,0())
s(max(___y110,___y109)) -> max(s(___y110),s(___y109))
max(0(),___y113) -> ___y113
max(___y117,0()) -> ___y117
max(s(___y122),s(___y121)) -> s(max(___y122,___y121))