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=3
   
   interpretation:
    [q3#](x0) = [1 0 1]x0,
    
    [q2#](x0) = [1 0 0]x0 + [1],
    
    [1'#](x0) = [1 1 0]x0,
    
    [0#](x0) = [1 1 0]x0,
    
    [0'#](x0) = [1 1 0]x0,
    
    [q1#](x0) = [1 1 1]x0,
    
    [q0#](x0) = [1 1 1]x0,
    
               [0 0 0]  
    [q4](x0) = [1 0 0]x0
               [0 1 0]  ,
    
              [0 0 0]  
    [b](x0) = [0 0 0]x0
              [1 1 1]  ,
    
               [0 0 0]  
    [q3](x0) = [0 0 0]x0
               [0 0 1]  ,
    
               [1 0 1]     [1]
    [q2](x0) = [0 1 1]x0 + [0]
               [0 0 0]     [0],
    
              [1 1 1]     [1]
    [1](x0) = [0 1 1]x0 + [1]
              [0 0 0]     [0],
    
               [1 1 0]     [0]
    [1'](x0) = [1 0 0]x0 + [0]
               [0 0 1]     [1],
    
               [1 1 1]  
    [0'](x0) = [0 0 0]x0
               [0 0 0]  ,
    
               [1 1 0]  
    [q1](x0) = [1 0 0]x0
               [0 0 1]  ,
    
               [1 1 0]  
    [q0](x0) = [0 0 0]x0
               [0 0 1]  ,
    
              [1 1 1]     [0]
    [0](x0) = [1 0 0]x0 + [0]
              [0 0 0]     [1]
   orientation:
    q0#(0(x1)) = [2 1 1]x1 + [1] >= [1 1 1]x1 = q1#(x1)
    
    q0#(0(x1)) = [2 1 1]x1 + [1] >= [2 1 0]x1 = 0'#(q1(x1))
    
    q1#(0(x1)) = [2 1 1]x1 + [1] >= [1 1 1]x1 = q1#(x1)
    
    q1#(0(x1)) = [2 1 1]x1 + [1] >= [2 1 0]x1 = 0#(q1(x1))
    
    q1#(1'(x1)) = [2 1 1]x1 + [1] >= [1 1 1]x1 = q1#(x1)
    
    q1#(1'(x1)) = [2 1 1]x1 + [1] >= [2 1 0]x1 = 1'#(q1(x1))
    
    0#(q1(1(x1))) = [2 3 3]x1 + [3] >= [1 1 0]x1 = 1'#(x1)
    
    0#(q1(1(x1))) = [2 3 3]x1 + [3] >= [2 1 0]x1 = 0#(1'(x1))
    
    0#(q1(1(x1))) = [2 3 3]x1 + [3] >= [2 1 1]x1 + [2] = q2#(0(1'(x1)))
    
    0'#(q1(1(x1))) = [2 3 3]x1 + [3] >= [1 1 0]x1 = 1'#(x1)
    
    0'#(q1(1(x1))) = [2 3 3]x1 + [3] >= [2 1 0]x1 = 0'#(1'(x1))
    
    0'#(q1(1(x1))) = [2 3 3]x1 + [3] >= [2 1 1]x1 + [2] = q2#(0'(1'(x1)))
    
    1'#(q1(1(x1))) = [2 3 3]x1 + [3] >= [1 1 0]x1 = 1'#(x1)
    
    1'#(q1(1(x1))) = [2 3 3]x1 + [3] >= [2 1 0]x1 = 1'#(1'(x1))
    
    1'#(q1(1(x1))) = [2 3 3]x1 + [3] >= [2 1 0]x1 + [1] = q2#(1'(1'(x1)))
    
    0#(q2(0(x1))) = [2 1 1]x1 + [3] >= [2 1 1]x1 = 0#(0(x1))
    
    0#(q2(0(x1))) = [2 1 1]x1 + [3] >= [2 1 1]x1 + [2] = q2#(0(0(x1)))
    
    0'#(q2(0(x1))) = [2 1 1]x1 + [3] >= [2 1 1]x1 = 0'#(0(x1))
    
    0'#(q2(0(x1))) = [2 1 1]x1 + [3] >= [2 1 1]x1 + [2] = q2#(0'(0(x1)))
    
    1'#(q2(0(x1))) = [2 1 1]x1 + [3] >= [2 1 1]x1 = 1'#(0(x1))
    
    1'#(q2(0(x1))) = [2 1 1]x1 + [3] >= [2 1 1]x1 + [1] = q2#(1'(0(x1)))
    
    0#(q2(1'(x1))) = [2 1 2]x1 + [3] >= [2 1 0]x1 = 0#(1'(x1))
    
    0#(q2(1'(x1))) = [2 1 2]x1 + [3] >= [2 1 1]x1 + [2] = q2#(0(1'(x1)))
    
    0'#(q2(1'(x1))) = [2 1 2]x1 + [3] >= [2 1 0]x1 = 0'#(1'(x1))
    
    0'#(q2(1'(x1))) = [2 1 2]x1 + [3] >= [2 1 1]x1 + [2] = q2#(0'(1'(x1)))
    
    1'#(q2(1'(x1))) = [2 1 2]x1 + [3] >= [2 1 0]x1 = 1'#(1'(x1))
    
    1'#(q2(1'(x1))) = [2 1 2]x1 + [3] >= [2 1 0]x1 + [1] = q2#(1'(1'(x1)))
    
    q2#(0'(x1)) = [1 1 1]x1 + [1] >= [1 1 1]x1 = q0#(x1)
    
    q2#(0'(x1)) = [1 1 1]x1 + [1] >= [1 1 0]x1 = 0'#(q0(x1))
    
    q0#(1'(x1)) = [2 1 1]x1 + [1] >= [1 0 1]x1 = q3#(x1)
    
    q0#(1'(x1)) = [2 1 1]x1 + [1] >= [0] = 1'#(q3(x1))
    
    q3#(1'(x1)) = [1 1 1]x1 + [1] >= [1 0 1]x1 = q3#(x1)
    
    q3#(1'(x1)) = [1 1 1]x1 + [1] >= [0] = 1'#(q3(x1))
    
                [2 1 1]     [0]    [2 1 1]               
    q0(0(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = 0'(q1(x1))
                [0 0 0]     [1]    [0 0 0]               
    
                [2 1 1]     [0]    [2 1 1]     [0]            
    q1(0(x1)) = [1 1 1]x1 + [0] >= [1 1 0]x1 + [0] = 0(q1(x1))
                [0 0 0]     [1]    [0 0 0]     [1]            
    
                 [2 1 0]     [0]    [2 1 0]     [0]             
    q1(1'(x1)) = [1 1 0]x1 + [0] >= [1 1 0]x1 + [0] = 1'(q1(x1))
                 [0 0 1]     [1]    [0 0 1]     [1]             
    
                   [2 3 3]     [3]    [2 1 1]     [3]                
    0(q1(1(x1))) = [1 2 2]x1 + [2] >= [1 1 0]x1 + [1] = q2(0(1'(x1)))
                   [0 0 0]     [1]    [0 0 0]     [0]                
    
                    [2 3 3]     [3]    [2 1 1]     [2]                 
    0'(q1(1(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = q2(0'(1'(x1)))
                    [0 0 0]     [0]    [0 0 0]     [0]                 
    
                    [2 3 3]     [3]    [2 1 1]     [3]                 
    1'(q1(1(x1))) = [1 2 2]x1 + [2] >= [1 1 1]x1 + [2] = q2(1'(1'(x1)))
                    [0 0 0]     [1]    [0 0 0]     [0]                 
    
                   [2 1 1]     [3]    [2 1 1]     [3]               
    0(q2(0(x1))) = [1 1 1]x1 + [2] >= [1 1 1]x1 + [1] = q2(0(0(x1)))
                   [0 0 0]     [1]    [0 0 0]     [0]               
    
                    [2 1 1]     [3]    [2 1 1]     [2]                
    0'(q2(0(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = q2(0'(0(x1)))
                    [0 0 0]     [0]    [0 0 0]     [0]                
    
                    [2 1 1]     [3]    [2 1 1]     [3]                
    1'(q2(0(x1))) = [1 1 1]x1 + [2] >= [1 1 1]x1 + [2] = q2(1'(0(x1)))
                    [0 0 0]     [1]    [0 0 0]     [0]                
    
                    [2 1 2]     [3]    [2 1 1]     [3]                
    0(q2(1'(x1))) = [1 1 1]x1 + [2] >= [1 1 0]x1 + [1] = q2(0(1'(x1)))
                    [0 0 0]     [1]    [0 0 0]     [0]                
    
                     [2 1 2]     [3]    [2 1 1]     [2]                 
    0'(q2(1'(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = q2(0'(1'(x1)))
                     [0 0 0]     [0]    [0 0 0]     [0]                 
    
                     [2 1 2]     [3]    [2 1 1]     [3]                 
    1'(q2(1'(x1))) = [1 1 1]x1 + [2] >= [1 1 1]x1 + [2] = q2(1'(1'(x1)))
                     [0 0 0]     [1]    [0 0 0]     [0]                 
    
                 [1 1 1]     [1]    [1 1 1]               
    q2(0'(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = 0'(q0(x1))
                 [0 0 0]     [0]    [0 0 0]               
    
                 [2 1 0]     [0]    [0 0 0]     [0]             
    q0(1'(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = 1'(q3(x1))
                 [0 0 1]     [1]    [0 0 1]     [1]             
    
                 [0 0 0]     [0]    [0 0 0]     [0]             
    q3(1'(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = 1'(q3(x1))
                 [0 0 1]     [1]    [0 0 1]     [1]             
    
                [0 0 0]      [0 0 0]              
    q3(b(x1)) = [0 0 0]x1 >= [0 0 0]x1 = b(q4(x1))
                [1 1 1]      [1 1 0]              
   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