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:
 DP Processor:
  DPs:
   q0#(0(x1)) -> q1#(x1)
   q0#(0(x1)) -> 0'#(q1(x1))
   q1#(0(x1)) -> q1#(x1)
   q1#(0(x1)) -> 0#(q1(x1))
   q1#(1'(x1)) -> q1#(x1)
   q1#(1'(x1)) -> 1'#(q1(x1))
   0#(q1(1(x1))) -> 1'#(x1)
   0#(q1(1(x1))) -> 0#(1'(x1))
   0#(q1(1(x1))) -> q2#(0(1'(x1)))
   0'#(q1(1(x1))) -> 1'#(x1)
   0'#(q1(1(x1))) -> 0'#(1'(x1))
   0'#(q1(1(x1))) -> q2#(0'(1'(x1)))
   1'#(q1(1(x1))) -> 1'#(x1)
   1'#(q1(1(x1))) -> 1'#(1'(x1))
   1'#(q1(1(x1))) -> q2#(1'(1'(x1)))
   0#(q2(0(x1))) -> 0#(0(x1))
   0#(q2(0(x1))) -> q2#(0(0(x1)))
   0'#(q2(0(x1))) -> 0'#(0(x1))
   0'#(q2(0(x1))) -> q2#(0'(0(x1)))
   1'#(q2(0(x1))) -> 1'#(0(x1))
   1'#(q2(0(x1))) -> q2#(1'(0(x1)))
   0#(q2(1'(x1))) -> 0#(1'(x1))
   0#(q2(1'(x1))) -> q2#(0(1'(x1)))
   0'#(q2(1'(x1))) -> 0'#(1'(x1))
   0'#(q2(1'(x1))) -> q2#(0'(1'(x1)))
   1'#(q2(1'(x1))) -> 1'#(1'(x1))
   1'#(q2(1'(x1))) -> q2#(1'(1'(x1)))
   q2#(0'(x1)) -> q0#(x1)
   q2#(0'(x1)) -> 0'#(q0(x1))
   q0#(1'(x1)) -> q3#(x1)
   q0#(1'(x1)) -> 1'#(q3(x1))
   q3#(1'(x1)) -> q3#(x1)
   q3#(1'(x1)) -> 1'#(q3(x1))
  TRS:
   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))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [q3#](x0) = 8x0,
    
    [q2#](x0) = 2x0 + 3,
    
    [1'#](x0) = 4x0 + 8,
    
    [0#](x0) = 2x0 + 4,
    
    [0'#](x0) = 4x0,
    
    [q1#](x0) = 2x0 + 6,
    
    [q0#](x0) = 2x0 + 1,
    
    [q4](x0) = x0,
    
    [b](x0) = 4x0 + 18,
    
    [q3](x0) = x0,
    
    [q2](x0) = 2x0 + 5,
    
    [1](x0) = 8x0 + 13,
    
    [1'](x0) = 4x0 + 4,
    
    [0'](x0) = 4x0,
    
    [q1](x0) = x0,
    
    [q0](x0) = 2x0,
    
    [0](x0) = 2x0 + 4
   orientation:
    q0#(0(x1)) = 4x1 + 9 >= 2x1 + 6 = q1#(x1)
    
    q0#(0(x1)) = 4x1 + 9 >= 4x1 = 0'#(q1(x1))
    
    q1#(0(x1)) = 4x1 + 14 >= 2x1 + 6 = q1#(x1)
    
    q1#(0(x1)) = 4x1 + 14 >= 2x1 + 4 = 0#(q1(x1))
    
    q1#(1'(x1)) = 8x1 + 14 >= 2x1 + 6 = q1#(x1)
    
    q1#(1'(x1)) = 8x1 + 14 >= 4x1 + 8 = 1'#(q1(x1))
    
    0#(q1(1(x1))) = 16x1 + 30 >= 4x1 + 8 = 1'#(x1)
    
    0#(q1(1(x1))) = 16x1 + 30 >= 8x1 + 12 = 0#(1'(x1))
    
    0#(q1(1(x1))) = 16x1 + 30 >= 16x1 + 27 = q2#(0(1'(x1)))
    
    0'#(q1(1(x1))) = 32x1 + 52 >= 4x1 + 8 = 1'#(x1)
    
    0'#(q1(1(x1))) = 32x1 + 52 >= 16x1 + 16 = 0'#(1'(x1))
    
    0'#(q1(1(x1))) = 32x1 + 52 >= 32x1 + 35 = q2#(0'(1'(x1)))
    
    1'#(q1(1(x1))) = 32x1 + 60 >= 4x1 + 8 = 1'#(x1)
    
    1'#(q1(1(x1))) = 32x1 + 60 >= 16x1 + 24 = 1'#(1'(x1))
    
    1'#(q1(1(x1))) = 32x1 + 60 >= 32x1 + 43 = q2#(1'(1'(x1)))
    
    0#(q2(0(x1))) = 8x1 + 30 >= 4x1 + 12 = 0#(0(x1))
    
    0#(q2(0(x1))) = 8x1 + 30 >= 8x1 + 27 = q2#(0(0(x1)))
    
    0'#(q2(0(x1))) = 16x1 + 52 >= 8x1 + 16 = 0'#(0(x1))
    
    0'#(q2(0(x1))) = 16x1 + 52 >= 16x1 + 35 = q2#(0'(0(x1)))
    
    1'#(q2(0(x1))) = 16x1 + 60 >= 8x1 + 24 = 1'#(0(x1))
    
    1'#(q2(0(x1))) = 16x1 + 60 >= 16x1 + 43 = q2#(1'(0(x1)))
    
    0#(q2(1'(x1))) = 16x1 + 30 >= 8x1 + 12 = 0#(1'(x1))
    
    0#(q2(1'(x1))) = 16x1 + 30 >= 16x1 + 27 = q2#(0(1'(x1)))
    
    0'#(q2(1'(x1))) = 32x1 + 52 >= 16x1 + 16 = 0'#(1'(x1))
    
    0'#(q2(1'(x1))) = 32x1 + 52 >= 32x1 + 35 = q2#(0'(1'(x1)))
    
    1'#(q2(1'(x1))) = 32x1 + 60 >= 16x1 + 24 = 1'#(1'(x1))
    
    1'#(q2(1'(x1))) = 32x1 + 60 >= 32x1 + 43 = q2#(1'(1'(x1)))
    
    q2#(0'(x1)) = 8x1 + 3 >= 2x1 + 1 = q0#(x1)
    
    q2#(0'(x1)) = 8x1 + 3 >= 8x1 = 0'#(q0(x1))
    
    q0#(1'(x1)) = 8x1 + 9 >= 8x1 = q3#(x1)
    
    q0#(1'(x1)) = 8x1 + 9 >= 4x1 + 8 = 1'#(q3(x1))
    
    q3#(1'(x1)) = 32x1 + 32 >= 8x1 = q3#(x1)
    
    q3#(1'(x1)) = 32x1 + 32 >= 4x1 + 8 = 1'#(q3(x1))
    
    q0(0(x1)) = 4x1 + 8 >= 4x1 = 0'(q1(x1))
    
    q1(0(x1)) = 2x1 + 4 >= 2x1 + 4 = 0(q1(x1))
    
    q1(1'(x1)) = 4x1 + 4 >= 4x1 + 4 = 1'(q1(x1))
    
    0(q1(1(x1))) = 16x1 + 30 >= 16x1 + 29 = q2(0(1'(x1)))
    
    0'(q1(1(x1))) = 32x1 + 52 >= 32x1 + 37 = q2(0'(1'(x1)))
    
    1'(q1(1(x1))) = 32x1 + 56 >= 32x1 + 45 = q2(1'(1'(x1)))
    
    0(q2(0(x1))) = 8x1 + 30 >= 8x1 + 29 = q2(0(0(x1)))
    
    0'(q2(0(x1))) = 16x1 + 52 >= 16x1 + 37 = q2(0'(0(x1)))
    
    1'(q2(0(x1))) = 16x1 + 56 >= 16x1 + 45 = q2(1'(0(x1)))
    
    0(q2(1'(x1))) = 16x1 + 30 >= 16x1 + 29 = q2(0(1'(x1)))
    
    0'(q2(1'(x1))) = 32x1 + 52 >= 32x1 + 37 = q2(0'(1'(x1)))
    
    1'(q2(1'(x1))) = 32x1 + 56 >= 32x1 + 45 = q2(1'(1'(x1)))
    
    q2(0'(x1)) = 8x1 + 5 >= 8x1 = 0'(q0(x1))
    
    q0(1'(x1)) = 8x1 + 8 >= 4x1 + 4 = 1'(q3(x1))
    
    q3(1'(x1)) = 4x1 + 4 >= 4x1 + 4 = 1'(q3(x1))
    
    q3(b(x1)) = 4x1 + 18 >= 4x1 + 18 = b(q4(x1))
   problem:
    DPs:
     
    TRS:
     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))
   Qed