YES

TRS:

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

max/plus interpretations on N:

  *_A(x1,x2) = max{13, 11, 5 + x2}
  *#_A(x1,x2) = max{0, 3, -1 + x2}
  otimes_A(x1,x2) = max{1, x1, 0}
  otimes#_A(x1,x2) = max{11, -1, -1}
  1_A = 0
  1#_A = 0
  +_A(x1,x2) = max{0, x1, 1 + x2}
  +#_A(x1,x2) = max{0, 0, 0}
  oplus_A(x1,x2) = max{2, x1, x2}
  oplus#_A(x1,x2) = max{2, -2, -2}

precedence:

  * = 1 = + > otimes = oplus