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{5, 1 + x1, 2 + x2}
  *#_A(x1,x2) = max{0, -5, -6}
  +_A(x1,x2) = max{4, 3, 5}
  +#_A(x1,x2) = max{0, -7, 0}
  1_A = 0
  1#_A = 0

precedence:

  * > + = 1