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:
 String Reversal Processor:
  0(1(x1)) -> 1(0(0(0(x1))))
  1(0(x1)) -> 1(x1)
  1(1(x1)) -> 0(0(0(0(x1))))
  0(0(x1)) -> 0(x1)
  KBO Processor:
   weight function:
    w0 = 1
    w(1) = 1
    w(0) = 0
   precedence:
    0 > 1
   problem:
    
   Qed