YES
Trs:
 {    .(e(), x) -> x,
  .(/(y, x), x) -> y,
      .(x, e()) -> x,
  .(x, \(x, y)) -> y,
  /(.(y, x), x) -> y,
      /(x, e()) -> x,
  /(x, \(y, x)) -> y,
        /(x, x) -> e(),
      \(e(), x) -> x,
  \(/(x, y), x) -> y,
  \(x, .(x, y)) -> y,
        \(x, x) -> e()}
 Comment:
  We consider a non-duplicating trs.
  BOUND:
   Automaton:
    {      e_1() -> q4,
           e_0() -> q4,
     ._0(q4, q4) -> q4,
     /_0(q4, q4) -> q4,
     \_0(q4, q4) -> q4}
   Strict:
   {}
   Qed