(VAR x y z)
(RULES
  +(x,0)  -> x
  +(x,s(y))  -> s(+(x,y))
  +(0,y)  -> y
  +(s(x),y)  -> s(+(x,y))
  *(x,0) -> 0
  *(x,s(y)) -> +(*(x,y),x)
  *(0,y) -> 0
  *(s(x),y) -> +(*(x,y),y)
  +(+(x,y),z) -> +(x,+(y,z))
  +(x,y) -> +(y,x)
  *(*(x,y),z) -> *(x,*(y,z))
  *(x,y) -> *(y,x)
  *(x,+(y,z)) -> +(*(x,y),*(x,z))
  *(+(x,y),z) -> +(*(x,z),*(y,z))
)
(COMMENT from the collection of \cite{AT2012})