YES

TRS:

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

max/plus interpretations on N:

  +_A(x1,x2) = max{5, x1, 6 + x2}
  +#_A(x1,x2) = max{0, 1, -2 + x2}
  *_A(x1,x2) = max{13, 7 + x1, 6 + x2}
  *#_A(x1,x2) = max{2, -3, -1}

precedence:

  + > *