NO

Problem:
 0(q0(0(x1))) -> 0(0(q0(x1)))
 0(q0(1(x1))) -> 0(1(q0(x1)))
 1(q0(0(x1))) -> 0(0(q1(x1)))
 1(q0(1(x1))) -> 0(1(q1(x1)))
 1(q1(0(x1))) -> 1(0(q1(x1)))
 1(q1(1(x1))) -> 1(1(q1(x1)))
 0(q1(0(x1))) -> 0(0(q2(x1)))
 0(q1(1(x1))) -> 0(1(q2(x1)))
 1(q2(0(x1))) -> 1(0(q2(x1)))
 1(q2(1(x1))) -> 1(1(q2(x1)))
 0(q2(x1)) -> q3(1(x1))
 1(q3(x1)) -> q3(1(x1))
 0(q3(x1)) -> q4(0(x1))
 1(q4(x1)) -> q4(1(x1))
 0(q4(0(x1))) -> 1(0(q5(x1)))
 0(q4(1(x1))) -> 1(1(q5(x1)))
 1(q5(0(x1))) -> 0(0(q1(x1)))
 1(q5(1(x1))) -> 0(1(q1(x1)))
 0(q5(x1)) -> q6(0(x1))
 1(q6(x1)) -> q6(1(x1))
 1(q7(0(x1))) -> 0(0(q8(x1)))
 1(q7(1(x1))) -> 0(1(q8(x1)))
 0(q8(x1)) -> 0(q0(x1))
 1(q8(0(x1))) -> 1(0(q8(x1)))
 1(q8(1(x1))) -> 1(1(q8(x1)))
 0(q6(x1)) -> q9(0(x1))
 0(q9(0(x1))) -> 1(0(q7(x1)))
 0(q9(1(x1))) -> 1(1(q7(x1)))
 1(q9(x1)) -> q9(1(x1))
 h(q0(x1)) -> h(0(q0(x1)))
 q0(h(x1)) -> q0(0(h(x1)))
 h(q1(x1)) -> h(0(q1(x1)))
 q1(h(x1)) -> q1(0(h(x1)))
 h(q2(x1)) -> h(0(q2(x1)))
 q2(h(x1)) -> q2(0(h(x1)))
 h(q3(x1)) -> h(0(q3(x1)))
 q3(h(x1)) -> q3(0(h(x1)))
 h(q4(x1)) -> h(0(q4(x1)))
 q4(h(x1)) -> q4(0(h(x1)))
 h(q5(x1)) -> h(0(q5(x1)))
 q5(h(x1)) -> q5(0(h(x1)))
 h(q6(x1)) -> h(0(q6(x1)))
 q6(h(x1)) -> q6(0(h(x1)))

Proof:
 Unfolding Processor:
  loop length: 2
  terms:
   0(q0(0(h(x161))))
   0(0(q0(h(x161))))
  context: 0([])
  substitution:
   x161 -> x161
  Qed