YES

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

Proof:
 KBO Processor:
  weight function:
   w0 = 1
   w($) = w(#) = w(1) = w(0) = w(*) = 1
  precedence:
   $ > # > 1 > 0 > *
  problem:
   
  Qed