YES

---- CR(R)
---- Hot decreasingness.
R:
s(p(x)) -> x
p(s(x)) -> x
+(x,0()) -> x
+(x,s(y)) -> s(+(x,y))
+(x,p(y)) -> p(+(x,y))
+(0(),y) -> y
+(p(x),y) -> p(+(x,y))
+(s(x),y) -> s(+(x,y))

C:
s(p(x)) -> x
p(s(x)) -> x
+(x,0()) -> x
+(x,s(y)) -> s(+(x,y))
+(x,p(y)) -> p(+(x,y))
+(0(),y) -> y
+(p(x),y) -> p(+(x,y))
+(s(x),y) -> s(+(x,y))

Label: