YES
TRS:
 {0(0(x)) -> 0(x),
  0(1(x)) -> 1(x),
  1(0(x)) -> 0(0(0(1(x)))),
  1(1(x)) -> 0(0(0(0(x))))}
 DP:
  Strict:
   {1#(0(x)) -> 0#(0(0(1(x)))),
    1#(0(x)) -> 0#(0(1(x))),
    1#(0(x)) -> 0#(1(x)),
    1#(0(x)) -> 1#(x),
    1#(1(x)) -> 0#(x),
    1#(1(x)) -> 0#(0(x)),
    1#(1(x)) -> 0#(0(0(x))),
    1#(1(x)) -> 0#(0(0(0(x))))}
  Weak:
  {0(0(x)) -> 0(x),
   0(1(x)) -> 1(x),
   1(0(x)) -> 0(0(0(1(x)))),
   1(1(x)) -> 0(0(0(0(x))))}
  EDG:
   {(1#(0(x)) -> 1#(x), 1#(0(x)) -> 0#(0(0(1(x)))))
    (1#(0(x)) -> 1#(x), 1#(0(x)) -> 0#(0(1(x))))
    (1#(0(x)) -> 1#(x), 1#(0(x)) -> 0#(1(x)))
    (1#(0(x)) -> 1#(x), 1#(0(x)) -> 1#(x))
    (1#(0(x)) -> 1#(x), 1#(1(x)) -> 0#(x))
    (1#(0(x)) -> 1#(x), 1#(1(x)) -> 0#(0(x)))
    (1#(0(x)) -> 1#(x), 1#(1(x)) -> 0#(0(0(x))))
    (1#(0(x)) -> 1#(x), 1#(1(x)) -> 0#(0(0(0(x)))))}
   SCCS:
    Scc:
     {1#(0(x)) -> 1#(x)}
    SCC:
     Strict:
      {1#(0(x)) -> 1#(x)}
     Weak:
     {0(0(x)) -> 0(x),
      0(1(x)) -> 1(x),
      1(0(x)) -> 0(0(0(1(x)))),
      1(1(x)) -> 0(0(0(0(x))))}
     SPSC:
      Simple Projection:
       pi(1#) = 0
      Strict:
       {}
      Qed