YES

TRS:

  *(x,+(y,z)) -> +(*(x,y),*(x,z))
  *(+(x,y),z) -> +(*(x,z),*(y,z))
  *(x,1()) -> x
  *(1(),y) -> y

linear polynomial interpretations on N:

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

precedence:

  * = + = 1