YES

---- CR(R)
---- [Jouannaud and Kirchner, 1986]
R:
+(+(x,y),z) -> +(x,+(y,z))
+(x,y) -> +(y,x)
*(+(x,y),z) -> +(*(x,z),*(y,z))
*(x,+(y,z)) -> +(*(x,y),*(x,z))
CP_AC(R):
+(*(x,+(y,z)),*(w,+(y,z))) -> +(*(+(x,w),y),*(+(x,w),z))
+(*(+(x,y),z),*(+(x,y),w)) -> +(*(x,+(z,w)),*(y,+(z,w)))