YES
Time: 0.000395
TRS:
 {      .(x, 1()) -> x,
        .(x, i x) -> 1(),
  .(y, .(i y, z)) -> z,
        .(1(), x) -> x,
        .(i x, x) -> 1(),
  .(i y, .(y, z)) -> z,
            i 1() -> 1(),
            i i x -> x}
 RUF:
  Strict:
   {}
  Weak:
   {}
  Qed