YES

TRS:

  *(i(x),x) -> 1()
  *(1(),y) -> y
  *(x,0()) -> 0()
  *(*(x,y),z) -> *(x,*(y,z))

max/plus interpretations on N:

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

precedence:

  * = i > 1 = 0