YES

TRS:

  ++(nil(),y) -> y
  ++(x,nil()) -> x
  ++(.(x,y),z) -> .(x,++(y,z))
  ++(++(x,y),z) -> ++(x,++(y,z))

max/plus interpretations on N:

  ++_A(x1,x2) = max{1, 1 + x1, x2}
  ++#_A(x1,x2) = max{1, -3, -1}
  nil_A = 0
  nil#_A = 0
  ._A(x1,x2) = max{3, 3 + x1, 4}
  .#_A(x1,x2) = max{0, -4, -2}

precedence:

  ++ > nil = .