YES

TRS:

  +(x,+(y,z)) -> +(+(x,y),z)
  +(*(x,y),+(x,z)) -> *(x,+(y,z))
  +(*(x,y),+(*(x,z),u)) -> +(*(x,+(y,z)),u)

linear polynomial interpretations on N:

  +_A(x1,x2) = x1 + x2 + 1
  +#_A(x1,x2) = x2
  *_A(x1,x2) = x1 + x2 + 1
  *#_A(x1,x2) = 0

precedence:

  + > *