YES

TRS:

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

linear polynomial interpretations on N:

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

precedence:

  + > f