YES

TRS:

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

max/plus interpretations on N:

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

precedence:

  * > + = 1