YES
Trs:
 {          i(1()) -> 1(),
           i(i(x)) -> x,
         .(1(), x) -> x,
        .(i(x), x) -> 1(),
  .(i(y), .(y, z)) -> z,
         .(x, 1()) -> x,
        .(x, i(x)) -> 1(),
  .(y, .(i(y), z)) -> z}
 Comment:
  We consider a non-duplicating trs.
  BOUND:
   Automaton:
    {      1_1() -> q3,
           1_0() -> q3,
         i_0(q3) -> q3,
     ._0(q3, q3) -> q3}
   Strict:
   {}
   Qed