YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1) = x1
  f#_A(x1) = 0
  +_A(x1,x2) = x1 + x2 + 1
  +#_A(x1,x2) = x2
  0_A = 1
  0#_A = 0

precedence:

  + = 0 > f