YES

Problem:
 1(0(x1)) -> 0(0(0(1(x1))))
 0(1(x1)) -> 1(x1)
 1(1(x1)) -> 0(0(0(0(x1))))
 0(0(x1)) -> 0(x1)

Proof:
 DP Processor:
  DPs:
   1#(0(x1)) -> 1#(x1)
   1#(0(x1)) -> 0#(1(x1))
   1#(0(x1)) -> 0#(0(1(x1)))
   1#(0(x1)) -> 0#(0(0(1(x1))))
   1#(1(x1)) -> 0#(x1)
   1#(1(x1)) -> 0#(0(x1))
   1#(1(x1)) -> 0#(0(0(x1)))
   1#(1(x1)) -> 0#(0(0(0(x1))))
  TRS:
   1(0(x1)) -> 0(0(0(1(x1))))
   0(1(x1)) -> 1(x1)
   1(1(x1)) -> 0(0(0(0(x1))))
   0(0(x1)) -> 0(x1)
  TDG Processor:
   DPs:
    1#(0(x1)) -> 1#(x1)
    1#(0(x1)) -> 0#(1(x1))
    1#(0(x1)) -> 0#(0(1(x1)))
    1#(0(x1)) -> 0#(0(0(1(x1))))
    1#(1(x1)) -> 0#(x1)
    1#(1(x1)) -> 0#(0(x1))
    1#(1(x1)) -> 0#(0(0(x1)))
    1#(1(x1)) -> 0#(0(0(0(x1))))
   TRS:
    1(0(x1)) -> 0(0(0(1(x1))))
    0(1(x1)) -> 1(x1)
    1(1(x1)) -> 0(0(0(0(x1))))
    0(0(x1)) -> 0(x1)
   graph:
    1#(0(x1)) -> 1#(x1) -> 1#(1(x1)) -> 0#(0(0(0(x1))))
    1#(0(x1)) -> 1#(x1) -> 1#(1(x1)) -> 0#(0(0(x1)))
    1#(0(x1)) -> 1#(x1) -> 1#(1(x1)) -> 0#(0(x1))
    1#(0(x1)) -> 1#(x1) -> 1#(1(x1)) -> 0#(x1)
    1#(0(x1)) -> 1#(x1) -> 1#(0(x1)) -> 0#(0(0(1(x1))))
    1#(0(x1)) -> 1#(x1) -> 1#(0(x1)) -> 0#(0(1(x1)))
    1#(0(x1)) -> 1#(x1) -> 1#(0(x1)) -> 0#(1(x1))
    1#(0(x1)) -> 1#(x1) -> 1#(0(x1)) -> 1#(x1)
   CDG Processor:
    DPs:
     1#(0(x1)) -> 1#(x1)
     1#(0(x1)) -> 0#(1(x1))
     1#(0(x1)) -> 0#(0(1(x1)))
     1#(0(x1)) -> 0#(0(0(1(x1))))
     1#(1(x1)) -> 0#(x1)
     1#(1(x1)) -> 0#(0(x1))
     1#(1(x1)) -> 0#(0(0(x1)))
     1#(1(x1)) -> 0#(0(0(0(x1))))
    TRS:
     1(0(x1)) -> 0(0(0(1(x1))))
     0(1(x1)) -> 1(x1)
     1(1(x1)) -> 0(0(0(0(x1))))
     0(0(x1)) -> 0(x1)
    graph:
     
    Qed