YES
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