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

linear polynomial interpretations on N:

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

precedence:

  0 > i > +