YES

TRS:

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

linear polynomial interpretations on N:

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

precedence:

  * = +