YES

TRS:

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

max/plus interpretations on N:

  i_A(x1) = max{1, 3 + x1}
  i#_A(x1) = max{5, 1 + x1}
  0_A = 4
  0#_A = 6
  +_A(x1,x2) = max{8, x1, 11 + x2}
  +#_A(x1,x2) = max{0, 4, 7 + x2}

precedence:

  i > + > 0