NO

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

Proof:
 Nonconfluence Processor:
  terms: 0(2(0(0(3(1(x)))))) *<- 0(0(1(0(x)))) ->* 0(2(0(4(1(0(x))))))
  Qed