YES

1 decompositions
 #0 -----------
   1: E(+(x,y)) -> *(E(x),E(y))
   2: E(0()) -> 1()
   3: +(x,0()) -> x
   4: +(0(),x) -> x
   5: *(x,1()) -> x
   6: *(1(),x) -> x
   7: +(+(x,y),z) -> +(x,+(y,z))
   8: +(x,+(y,z)) -> +(+(x,y),z)
   9: +(x,y) -> +(y,x)
  10: *(*(x,y),z) -> *(x,*(y,z))
  11: *(x,*(y,z)) -> *(*(x,y),z)
  12: *(x,y) -> *(y,x)

@Jouannaud and Kirchner's criterion
--- R
   1: E(+(x,y)) -> *(E(x),E(y))
   2: E(0()) -> 1()
   3: +(x,0()) -> x
   4: +(0(),x) -> x
   5: *(x,1()) -> x
   6: *(1(),x) -> x
   7: +(+(x,y),z) -> +(x,+(y,z))
   8: +(x,+(y,z)) -> +(+(x,y),z)
   9: +(x,y) -> +(y,x)
  10: *(*(x,y),z) -> *(x,*(y,z))
  11: *(x,*(y,z)) -> *(*(x,y),z)
  12: *(x,y) -> *(y,x)

--- S
   1: E(+(x,y)) -> *(E(x),E(y))
   2: E(0()) -> 1()
   3: +(x,0()) -> x
   4: +(0(),x) -> x
   5: *(x,1()) -> x
   6: *(1(),x) -> x
   7: +(+(x,y),z) -> +(x,+(y,z))
   8: +(x,+(y,z)) -> +(+(x,y),z)
   9: +(x,y) -> +(y,x)
  10: *(*(x,y),z) -> *(x,*(y,z))
  11: *(x,*(y,z)) -> *(*(x,y),z)
  12: *(x,y) -> *(y,x)