YES

TRS:

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

linear polynomial interpretations on N:

  +_A(x1,x2) = x1
  +#_A(x1,x2) = 0
  0_A = 0
  0#_A = 1
  i_A(x1) = x1 + 1
  i#_A(x1) = 2
  *_A(x1,x2) = x2 + 1
  *#_A(x1,x2) = 1

precedence:

  i > 0 > + = *