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(),y) -> y
+(s(x),y) -> s(+(x,y))
inc(x) -> s(x)
+(x,y) -> +(y,x)
inc(+(x,y)) -> +(inc(x),y)

CP(R):
0() -> 0()
s(___y9) -> s(+(___y9,0()))
___y13 -> +(0(),___y13)
inc(___y16) -> +(inc(___y16),0())
s(+(0(),___y27)) -> s(___y27)
s(+(s(___y31),___y30)) -> s(+(___y31,s(___y30)))
s(+(___y36,___y37)) -> +(s(___y37),___y36)
inc(s(+(___y40,___y41))) -> +(inc(___y40),s(___y41))
0() -> 0()
s(___y48) -> s(+(0(),___y48))
___y56 -> +(___y56,0())
inc(___y59) -> +(inc(0()),___y59)
s(+(___y62,0())) -> s(___y62)
s(+(___y65,s(___y68))) -> s(+(s(___y65),___y68))
s(+(___y79,___y80)) -> +(___y80,s(___y79))
inc(s(+(___y83,___y84))) -> +(inc(s(___y83)),___y84)
s(+(___y103,___y104)) -> +(inc(___y103),___y104)
+(0(),___y105) -> ___y105
+(s(___y111),___y108) -> s(+(___y108,___y111))
+(___y113,0()) -> ___y113
+(___y116,s(___y117)) -> s(+(___y117,___y116))
inc(+(___y127,___y126)) -> +(inc(___y126),___y127)
+(inc(___y144),___y145) -> s(+(___y144,___y145))

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

CR(C): see below.

---- CR(R)
---- R : linear and strongly closed [Huet, 1980]
R:
+(x,0()) -> x
+(x,s(y)) -> s(+(x,y))
+(0(),y) -> y
+(s(x),y) -> s(+(x,y))
inc(x) -> s(x)
+(x,y) -> +(y,x)
CP(R):
0() -> 0()
s(___y1377) -> s(+(___y1377,0()))
___y1381 -> +(0(),___y1381)
s(+(0(),___y1392)) -> s(___y1392)
s(+(s(___y1396),___y1395)) -> s(+(___y1396,s(___y1395)))
s(+(___y1401,___y1402)) -> +(s(___y1402),___y1401)
0() -> 0()
s(___y1409) -> s(+(0(),___y1409))
___y1417 -> +(___y1417,0())
s(+(___y1420,0())) -> s(___y1420)
s(+(___y1423,s(___y1426))) -> s(+(s(___y1423),___y1426))
s(+(___y1437,___y1438)) -> +(___y1438,s(___y1437))
+(0(),___y1456) -> ___y1456
+(s(___y1462),___y1459) -> s(+(___y1459,___y1462))
+(___y1464,0()) -> ___y1464
+(___y1467,s(___y1468)) -> s(+(___y1468,___y1467))