YES

Problem:
 0(1(2(2(3(0(4(4(x1)))))))) -> 0(4(5(0(3(4(0(4(x1))))))))
 0(2(2(2(0(5(2(5(4(x1))))))))) -> 0(0(0(3(4(3(0(1(0(x1)))))))))
 2(1(1(3(4(3(1(1(5(x1))))))))) -> 1(0(2(3(1(0(5(1(5(x1)))))))))
 5(4(0(4(3(3(1(2(5(3(0(x1))))))))))) -> 5(5(2(5(3(1(5(0(3(5(2(x1)))))))))))
 2(4(5(0(1(1(3(3(5(3(0(0(x1)))))))))))) -> 4(4(2(2(1(0(4(0(1(3(2(0(x1))))))))))))
 4(4(3(0(3(1(5(3(5(1(3(1(5(3(x1)))))))))))))) -> 0(2(4(5(0(0(0(5(1(0(5(4(4(x1)))))))))))))
 2(2(0(0(2(1(0(5(3(2(2(1(4(0(5(x1))))))))))))))) -> 0(0(3(5(3(0(4(3(1(3(0(2(5(5(x1))))))))))))))
 3(0(0(4(2(5(5(1(3(0(2(3(3(5(1(4(5(x1))))))))))))))))) ->
 3(4(0(1(0(5(5(3(1(4(0(3(5(3(2(2(5(x1)))))))))))))))))
 5(1(1(4(1(5(3(0(4(3(2(5(4(1(3(3(5(x1))))))))))))))))) ->
 5(0(1(0(4(0(2(4(5(1(5(4(1(5(3(3(5(x1)))))))))))))))))
 0(1(4(4(3(2(0(4(1(4(3(4(4(1(5(3(4(4(x1)))))))))))))))))) ->
 0(2(4(2(3(1(0(1(1(1(3(0(2(4(4(1(1(2(x1))))))))))))))))))
 1(1(4(1(0(1(0(3(3(4(4(1(5(4(0(4(4(5(5(3(x1)))))))))))))))))))) ->
 1(3(0(3(2(2(4(4(2(0(3(3(4(0(3(0(4(3(4(0(x1))))))))))))))))))))
 2(0(3(3(3(4(1(1(0(4(4(0(3(3(3(0(0(1(5(3(x1)))))))))))))))))))) ->
 5(3(3(1(4(0(4(5(4(4(4(2(4(3(1(1(1(5(4(x1)))))))))))))))))))
 2(3(3(2(1(5(0(5(0(1(3(3(2(5(1(5(0(3(0(5(x1)))))))))))))))))))) ->
 3(4(0(2(5(5(2(4(2(4(3(1(1(4(4(5(5(3(5(x1)))))))))))))))))))
 3(3(2(2(3(3(4(0(0(0(2(5(0(5(3(0(0(1(1(4(x1)))))))))))))))))))) ->
 3(1(1(0(3(3(5(4(2(2(1(0(1(1(0(5(0(3(4(0(x1))))))))))))))))))))
 4(2(4(1(0(5(0(4(1(0(3(0(2(5(4(3(5(3(5(3(x1)))))))))))))))))))) ->
 4(2(5(4(4(2(4(5(0(0(3(1(5(0(2(0(2(2(1(x1)))))))))))))))))))

Proof:
 String Reversal Processor:
  4(4(0(3(2(2(1(0(x1)))))))) -> 4(0(4(3(0(5(4(0(x1))))))))
  4(5(2(5(0(2(2(2(0(x1))))))))) -> 0(1(0(3(4(3(0(0(0(x1)))))))))
  5(1(1(3(4(3(1(1(2(x1))))))))) -> 5(1(5(0(1(3(2(0(1(x1)))))))))
  0(3(5(2(1(3(3(4(0(4(5(x1))))))))))) -> 2(5(3(0(5(1(3(5(2(5(5(x1)))))))))))
  0(0(3(5(3(3(1(1(0(5(4(2(x1)))))))))))) -> 0(2(3(1(0(4(0(1(2(2(4(4(x1))))))))))))
  3(5(1(3(1(5(3(5(1(3(0(3(4(4(x1)))))))))))))) -> 4(4(5(0(1(5(0(0(0(5(4(2(0(x1)))))))))))))
  5(0(4(1(2(2(3(5(0(1(2(0(0(2(2(x1))))))))))))))) -> 5(5(2(0(3(1(3(4(0(3(5(3(0(0(x1))))))))))))))
  5(4(1(5(3(3(2(0(3(1(5(5(2(4(0(0(3(x1))))))))))))))))) ->
  5(2(2(3(5(3(0(4(1(3(5(5(0(1(0(4(3(x1)))))))))))))))))
  5(3(3(1(4(5(2(3(4(0(3(5(1(4(1(1(5(x1))))))))))))))))) ->
  5(3(3(5(1(4(5(1(5(4(2(0(4(0(1(0(5(x1)))))))))))))))))
  4(4(3(5(1(4(4(3(4(1(4(0(2(3(4(4(1(0(x1)))))))))))))))))) ->
  2(1(1(4(4(2(0(3(1(1(1(0(1(3(2(4(2(0(x1))))))))))))))))))
  3(5(5(4(4(0(4(5(1(4(4(3(3(0(1(0(1(4(1(1(x1)))))))))))))))))))) ->
  0(4(3(4(0(3(0(4(3(3(0(2(4(4(2(2(3(0(3(1(x1))))))))))))))))))))
  3(5(1(0(0(3(3(3(0(4(4(0(1(1(4(3(3(3(0(2(x1)))))))))))))))))))) ->
  4(5(1(1(1(3(4(2(4(4(4(5(4(0(4(1(3(3(5(x1)))))))))))))))))))
  5(0(3(0(5(1(5(2(3(3(1(0(5(0(5(1(2(3(3(2(x1)))))))))))))))))))) ->
  5(3(5(5(4(4(1(1(3(4(2(4(2(5(5(2(0(4(3(x1)))))))))))))))))))
  4(1(1(0(0(3(5(0(5(2(0(0(0(4(3(3(2(2(3(3(x1)))))))))))))))))))) ->
  0(4(3(0(5(0(1(1(0(1(2(2(4(5(3(3(0(1(1(3(x1))))))))))))))))))))
  3(5(3(5(3(4(5(2(0(3(0(1(4(0(5(0(1(4(2(4(x1)))))))))))))))))))) ->
  1(2(2(0(2(0(5(1(3(0(0(5(4(2(4(4(5(2(4(x1)))))))))))))))))))
  KBO Processor:
   weight function:
    w0 = 1
    w(5) = w(1) = w(2) = w(3) = w(0) = w(4) = 1
   precedence:
    4 > 3 > 0 > 2 > 1 > 5
   problem:
    
   Qed