YES

TRS:

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

linear polynomial interpretations on N:

  +_A(x1,x2) = x1 + 1
  +#_A(x1,x2) = 1
  *_A(x1,x2) = 1
  *#_A(x1,x2) = 0
  a_A = 1
  a#_A = 2

precedence:

  + > a > *