YES

TRS:

  +(x,0()) -> x
  +(x,i(x)) -> 0()
  +(+(x,y),z) -> +(x,+(y,z))
  *(x,+(y,z)) -> +(*(x,y),*(x,z))
  *(+(x,y),z) -> +(*(x,z),*(y,z))

max/plus interpretations on N:

  +_A(x1,x2) = max{0, x1, x2}
  +#_A(x1,x2) = max{0, x1, x2}
  0_A = 0
  0#_A = 0
  i_A(x1) = max{0, x1}
  i#_A(x1) = max{0, x1}
  *_A(x1,x2) = max{0, x1, x2}
  *#_A(x1,x2) = max{0, x1, x2}

precedence:

  * > + > 0 > i