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))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [q4](x0) = 1x0,
    
    [b](x0) = 15x0,
    
    [q3](x0) = 10x0,
    
    [q2](x0) = 3x0,
    
    [1](x0) = 7x0,
    
    [1'](x0) = 4x0,
    
    [0'](x0) = 13x0,
    
    [q1](x0) = x0,
    
    [q0](x0) = 9x0,
    
    [0](x0) = 4x0
   orientation:
    q0(0(x1)) = 13x1 >= 13x1 = 0'(q1(x1))
    
    q1(0(x1)) = 4x1 >= 4x1 = 0(q1(x1))
    
    q1(1'(x1)) = 4x1 >= 4x1 = 1'(q1(x1))
    
    0(q1(1(x1))) = 11x1 >= 11x1 = q2(0(1'(x1)))
    
    0'(q1(1(x1))) = 20x1 >= 20x1 = q2(0'(1'(x1)))
    
    1'(q1(1(x1))) = 11x1 >= 11x1 = q2(1'(1'(x1)))
    
    0(q2(0(x1))) = 11x1 >= 11x1 = q2(0(0(x1)))
    
    0'(q2(0(x1))) = 20x1 >= 20x1 = q2(0'(0(x1)))
    
    1'(q2(0(x1))) = 11x1 >= 11x1 = q2(1'(0(x1)))
    
    0(q2(1'(x1))) = 11x1 >= 11x1 = q2(0(1'(x1)))
    
    0'(q2(1'(x1))) = 20x1 >= 20x1 = q2(0'(1'(x1)))
    
    1'(q2(1'(x1))) = 11x1 >= 11x1 = q2(1'(1'(x1)))
    
    q3(1'(x1)) = 14x1 >= 14x1 = 1'(q3(x1))
    
    q3(b(x1)) = 25x1 >= 16x1 = 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))
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [q3](x0) = 1x0,
     
     [q2](x0) = 1x0,
     
     [1](x0) = 1x0,
     
     [1'](x0) = x0,
     
     [0'](x0) = 6x0,
     
     [q1](x0) = x0,
     
     [q0](x0) = 15x0,
     
     [0](x0) = 1x0
    orientation:
     q0(0(x1)) = 16x1 >= 6x1 = 0'(q1(x1))
     
     q1(0(x1)) = 1x1 >= 1x1 = 0(q1(x1))
     
     q1(1'(x1)) = x1 >= x1 = 1'(q1(x1))
     
     0(q1(1(x1))) = 2x1 >= 2x1 = q2(0(1'(x1)))
     
     0'(q1(1(x1))) = 7x1 >= 7x1 = q2(0'(1'(x1)))
     
     1'(q1(1(x1))) = 1x1 >= 1x1 = q2(1'(1'(x1)))
     
     0(q2(0(x1))) = 3x1 >= 3x1 = q2(0(0(x1)))
     
     0'(q2(0(x1))) = 8x1 >= 8x1 = q2(0'(0(x1)))
     
     1'(q2(0(x1))) = 2x1 >= 2x1 = q2(1'(0(x1)))
     
     0(q2(1'(x1))) = 2x1 >= 2x1 = q2(0(1'(x1)))
     
     0'(q2(1'(x1))) = 7x1 >= 7x1 = q2(0'(1'(x1)))
     
     1'(q2(1'(x1))) = 1x1 >= 1x1 = q2(1'(1'(x1)))
     
     q3(1'(x1)) = 1x1 >= 1x1 = 1'(q3(x1))
    problem:
     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))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [q3](x0) = x0,
      
      [q2](x0) = x0,
      
      [1](x0) = 7x0,
      
      [1'](x0) = x0,
      
      [0'](x0) = 4x0,
      
      [q1](x0) = x0,
      
      [0](x0) = 4x0
     orientation:
      q1(0(x1)) = 4x1 >= 4x1 = 0(q1(x1))
      
      q1(1'(x1)) = x1 >= x1 = 1'(q1(x1))
      
      0(q1(1(x1))) = 11x1 >= 4x1 = q2(0(1'(x1)))
      
      0'(q1(1(x1))) = 11x1 >= 4x1 = q2(0'(1'(x1)))
      
      1'(q1(1(x1))) = 7x1 >= x1 = q2(1'(1'(x1)))
      
      0(q2(0(x1))) = 8x1 >= 8x1 = q2(0(0(x1)))
      
      0'(q2(0(x1))) = 8x1 >= 8x1 = q2(0'(0(x1)))
      
      1'(q2(0(x1))) = 4x1 >= 4x1 = q2(1'(0(x1)))
      
      0(q2(1'(x1))) = 4x1 >= 4x1 = q2(0(1'(x1)))
      
      0'(q2(1'(x1))) = 4x1 >= 4x1 = q2(0'(1'(x1)))
      
      1'(q2(1'(x1))) = x1 >= x1 = q2(1'(1'(x1)))
      
      q3(1'(x1)) = x1 >= x1 = 1'(q3(x1))
     problem:
      q1(0(x1)) -> 0(q1(x1))
      q1(1'(x1)) -> 1'(q1(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))
     KBO Processor:
      weight function:
       w0 = 1
       w(q3) = w(q2) = w(1') = w(0') = w(q1) = w(0) = 1
      precedence:
       q1 > q3 > 1' ~ 0 > 0' > q2
      problem:
       
      Qed