YES

Problem:
 q0(0(x1)) -> 0'(q1(x1))
 q1(0(x1)) -> 0(q1(x1))
 q1(1'(x1)) -> 1'(q1(x1))
 0(q1(1(x1))) -> q2(0(1'(x1)))
 0'(q1(1(x1))) -> q2(0'(1'(x1)))
 1'(q1(1(x1))) -> q2(1'(1'(x1)))
 0(q2(0(x1))) -> q2(0(0(x1)))
 0'(q2(0(x1))) -> q2(0'(0(x1)))
 1'(q2(0(x1))) -> q2(1'(0(x1)))
 0(q2(1'(x1))) -> q2(0(1'(x1)))
 0'(q2(1'(x1))) -> q2(0'(1'(x1)))
 1'(q2(1'(x1))) -> q2(1'(1'(x1)))
 q2(0'(x1)) -> 0'(q0(x1))
 q0(1'(x1)) -> 1'(q3(x1))
 q3(1'(x1)) -> 1'(q3(x1))
 q3(b(x1)) -> b(q4(x1))

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [q4](x0) = x0,
   
   [b](x0) = 8x0,
   
   [q3](x0) = x0,
   
   [q2](x0) = 5x0,
   
   [1](x0) = 7x0,
   
   [1'](x0) = 4x0,
   
   [0'](x0) = 1x0,
   
   [q1](x0) = 2x0,
   
   [q0](x0) = 3x0,
   
   [0](x0) = x0
  orientation:
   q0(0(x1)) = 3x1 >= 3x1 = 0'(q1(x1))
   
   q1(0(x1)) = 2x1 >= 2x1 = 0(q1(x1))
   
   q1(1'(x1)) = 6x1 >= 6x1 = 1'(q1(x1))
   
   0(q1(1(x1))) = 9x1 >= 9x1 = q2(0(1'(x1)))
   
   0'(q1(1(x1))) = 10x1 >= 10x1 = q2(0'(1'(x1)))
   
   1'(q1(1(x1))) = 13x1 >= 13x1 = q2(1'(1'(x1)))
   
   0(q2(0(x1))) = 5x1 >= 5x1 = q2(0(0(x1)))
   
   0'(q2(0(x1))) = 6x1 >= 6x1 = q2(0'(0(x1)))
   
   1'(q2(0(x1))) = 9x1 >= 9x1 = q2(1'(0(x1)))
   
   0(q2(1'(x1))) = 9x1 >= 9x1 = q2(0(1'(x1)))
   
   0'(q2(1'(x1))) = 10x1 >= 10x1 = q2(0'(1'(x1)))
   
   1'(q2(1'(x1))) = 13x1 >= 13x1 = q2(1'(1'(x1)))
   
   q2(0'(x1)) = 6x1 >= 4x1 = 0'(q0(x1))
   
   q0(1'(x1)) = 7x1 >= 4x1 = 1'(q3(x1))
   
   q3(1'(x1)) = 4x1 >= 4x1 = 1'(q3(x1))
   
   q3(b(x1)) = 8x1 >= 8x1 = b(q4(x1))
  problem:
   q0(0(x1)) -> 0'(q1(x1))
   q1(0(x1)) -> 0(q1(x1))
   q1(1'(x1)) -> 1'(q1(x1))
   0(q1(1(x1))) -> q2(0(1'(x1)))
   0'(q1(1(x1))) -> q2(0'(1'(x1)))
   1'(q1(1(x1))) -> q2(1'(1'(x1)))
   0(q2(0(x1))) -> q2(0(0(x1)))
   0'(q2(0(x1))) -> q2(0'(0(x1)))
   1'(q2(0(x1))) -> q2(1'(0(x1)))
   0(q2(1'(x1))) -> q2(0(1'(x1)))
   0'(q2(1'(x1))) -> q2(0'(1'(x1)))
   1'(q2(1'(x1))) -> q2(1'(1'(x1)))
   q3(1'(x1)) -> 1'(q3(x1))
   q3(b(x1)) -> b(q4(x1))
  KBO Processor:
   weight function:
    w0 = 1
    w(q4) = w(b) = w(q3) = w(q2) = w(1) = w(1') = w(q1) = w(q0) = w(0) = 1
    w(0') = 0
   precedence:
    0' > q3 ~ q1 > 1' ~ 0 > q4 ~ b ~ q2 ~ 1 ~ q0
   problem:
    
   Qed