YES

1 decompositions
 #0 -----------
   1: +(+(x,y),z) -> +(x,+(y,z))
   2: +(x,y) -> +(y,x)
   3: *(+(x,y),z) -> +(*(x,z),*(y,z))
   4: *(x,+(y,z)) -> +(*(x,y),*(x,z))

@Jouannaud and Kirchner's criterion
--- R
   1: +(+(x,y),z) -> +(x,+(y,z))
   2: +(x,y) -> +(y,x)
   3: *(+(x,y),z) -> +(*(x,z),*(y,z))
   4: *(x,+(y,z)) -> +(*(x,y),*(x,z))

--- S
   1: +(+(x,y),z) -> +(x,+(y,z))
   2: +(x,y) -> +(y,x)
   3: *(+(x,y),z) -> +(*(x,z),*(y,z))
   4: *(x,+(y,z)) -> +(*(x,y),*(x,z))