YES

Problem:
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(#(x1)) -> #(x1)
 #(*(x1)) -> *(x1)

Proof:
 DP Processor:
  DPs:
   0#(*(x1)) -> 1#(x1)
   1#(*(x1)) -> ##(x1)
   1#(*(x1)) -> 0#(#(x1))
   ##(0(x1)) -> ##(x1)
   ##(0(x1)) -> 0#(#(x1))
   ##(1(x1)) -> ##(x1)
   ##(1(x1)) -> 1#(#(x1))
  TRS:
   0(*(x1)) -> *(1(x1))
   1(*(x1)) -> 0(#(x1))
   #(0(x1)) -> 0(#(x1))
   #(1(x1)) -> 1(#(x1))
   #($(x1)) -> *($(x1))
   #(#(x1)) -> #(x1)
   #(*(x1)) -> *(x1)
  TDG Processor:
   DPs:
    0#(*(x1)) -> 1#(x1)
    1#(*(x1)) -> ##(x1)
    1#(*(x1)) -> 0#(#(x1))
    ##(0(x1)) -> ##(x1)
    ##(0(x1)) -> 0#(#(x1))
    ##(1(x1)) -> ##(x1)
    ##(1(x1)) -> 1#(#(x1))
   TRS:
    0(*(x1)) -> *(1(x1))
    1(*(x1)) -> 0(#(x1))
    #(0(x1)) -> 0(#(x1))
    #(1(x1)) -> 1(#(x1))
    #($(x1)) -> *($(x1))
    #(#(x1)) -> #(x1)
    #(*(x1)) -> *(x1)
   graph:
    ##(1(x1)) -> ##(x1) -> ##(1(x1)) -> 1#(#(x1))
    ##(1(x1)) -> ##(x1) -> ##(1(x1)) -> ##(x1)
    ##(1(x1)) -> ##(x1) -> ##(0(x1)) -> 0#(#(x1))
    ##(1(x1)) -> ##(x1) -> ##(0(x1)) -> ##(x1)
    ##(1(x1)) -> 1#(#(x1)) -> 1#(*(x1)) -> 0#(#(x1))
    ##(1(x1)) -> 1#(#(x1)) -> 1#(*(x1)) -> ##(x1)
    ##(0(x1)) -> ##(x1) -> ##(1(x1)) -> 1#(#(x1))
    ##(0(x1)) -> ##(x1) -> ##(1(x1)) -> ##(x1)
    ##(0(x1)) -> ##(x1) -> ##(0(x1)) -> 0#(#(x1))
    ##(0(x1)) -> ##(x1) -> ##(0(x1)) -> ##(x1)
    ##(0(x1)) -> 0#(#(x1)) -> 0#(*(x1)) -> 1#(x1)
    1#(*(x1)) -> ##(x1) -> ##(1(x1)) -> 1#(#(x1))
    1#(*(x1)) -> ##(x1) -> ##(1(x1)) -> ##(x1)
    1#(*(x1)) -> ##(x1) -> ##(0(x1)) -> 0#(#(x1))
    1#(*(x1)) -> ##(x1) -> ##(0(x1)) -> ##(x1)
    1#(*(x1)) -> 0#(#(x1)) -> 0#(*(x1)) -> 1#(x1)
    0#(*(x1)) -> 1#(x1) -> 1#(*(x1)) -> 0#(#(x1))
    0#(*(x1)) -> 1#(x1) -> 1#(*(x1)) -> ##(x1)
   KBO Processor:
    weight function:
     w0 = 1
     w(##) = w(1#) = w($) = w(#) = w(1) = w(0) = w(*) = 1
     w(0#) = 0
    precedence:
     0# > # > ## ~ 1 > 0 > 1# ~ $ ~ *
    problem:
     DPs:
      
     TRS:
      
    Qed