YES

Problem:
 q0(a(x1)) -> x(q1(x1))
 q1(a(x1)) -> a(q1(x1))
 q1(y(x1)) -> y(q1(x1))
 a(q1(b(x1))) -> q2(a(y(x1)))
 a(q2(a(x1))) -> q2(a(a(x1)))
 a(q2(y(x1))) -> q2(a(y(x1)))
 y(q1(b(x1))) -> q2(y(y(x1)))
 y(q2(a(x1))) -> q2(y(a(x1)))
 y(q2(y(x1))) -> q2(y(y(x1)))
 q2(x(x1)) -> x(q0(x1))
 q0(y(x1)) -> y(q3(x1))
 q3(y(x1)) -> y(q3(x1))
 q3(bl(x1)) -> bl(q4(x1))

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [q4](x0) = x0,
   
   [bl](x0) = 2x0,
   
   [q3](x0) = 8x0,
   
   [q2](x0) = 8x0,
   
   [b](x0) = 12x0,
   
   [y](x0) = 4x0,
   
   [x](x0) = 8x0,
   
   [q1](x0) = x0,
   
   [q0](x0) = 8x0,
   
   [a](x0) = x0
  orientation:
   q0(a(x1)) = 8x1 >= 8x1 = x(q1(x1))
   
   q1(a(x1)) = x1 >= x1 = a(q1(x1))
   
   q1(y(x1)) = 4x1 >= 4x1 = y(q1(x1))
   
   a(q1(b(x1))) = 12x1 >= 12x1 = q2(a(y(x1)))
   
   a(q2(a(x1))) = 8x1 >= 8x1 = q2(a(a(x1)))
   
   a(q2(y(x1))) = 12x1 >= 12x1 = q2(a(y(x1)))
   
   y(q1(b(x1))) = 16x1 >= 16x1 = q2(y(y(x1)))
   
   y(q2(a(x1))) = 12x1 >= 12x1 = q2(y(a(x1)))
   
   y(q2(y(x1))) = 16x1 >= 16x1 = q2(y(y(x1)))
   
   q2(x(x1)) = 16x1 >= 16x1 = x(q0(x1))
   
   q0(y(x1)) = 12x1 >= 12x1 = y(q3(x1))
   
   q3(y(x1)) = 12x1 >= 12x1 = y(q3(x1))
   
   q3(bl(x1)) = 10x1 >= 2x1 = bl(q4(x1))
  problem:
   q0(a(x1)) -> x(q1(x1))
   q1(a(x1)) -> a(q1(x1))
   q1(y(x1)) -> y(q1(x1))
   a(q1(b(x1))) -> q2(a(y(x1)))
   a(q2(a(x1))) -> q2(a(a(x1)))
   a(q2(y(x1))) -> q2(a(y(x1)))
   y(q1(b(x1))) -> q2(y(y(x1)))
   y(q2(a(x1))) -> q2(y(a(x1)))
   y(q2(y(x1))) -> q2(y(y(x1)))
   q2(x(x1)) -> x(q0(x1))
   q0(y(x1)) -> y(q3(x1))
   q3(y(x1)) -> y(q3(x1))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [q3](x0) = x0,
    
    [q2](x0) = 2x0,
    
    [b](x0) = 14x0,
    
    [y](x0) = 12x0,
    
    [x](x0) = x0,
    
    [q1](x0) = x0,
    
    [q0](x0) = x0,
    
    [a](x0) = 4x0
   orientation:
    q0(a(x1)) = 4x1 >= x1 = x(q1(x1))
    
    q1(a(x1)) = 4x1 >= 4x1 = a(q1(x1))
    
    q1(y(x1)) = 12x1 >= 12x1 = y(q1(x1))
    
    a(q1(b(x1))) = 18x1 >= 18x1 = q2(a(y(x1)))
    
    a(q2(a(x1))) = 10x1 >= 10x1 = q2(a(a(x1)))
    
    a(q2(y(x1))) = 18x1 >= 18x1 = q2(a(y(x1)))
    
    y(q1(b(x1))) = 26x1 >= 26x1 = q2(y(y(x1)))
    
    y(q2(a(x1))) = 18x1 >= 18x1 = q2(y(a(x1)))
    
    y(q2(y(x1))) = 26x1 >= 26x1 = q2(y(y(x1)))
    
    q2(x(x1)) = 2x1 >= x1 = x(q0(x1))
    
    q0(y(x1)) = 12x1 >= 12x1 = y(q3(x1))
    
    q3(y(x1)) = 12x1 >= 12x1 = y(q3(x1))
   problem:
    q1(a(x1)) -> a(q1(x1))
    q1(y(x1)) -> y(q1(x1))
    a(q1(b(x1))) -> q2(a(y(x1)))
    a(q2(a(x1))) -> q2(a(a(x1)))
    a(q2(y(x1))) -> q2(a(y(x1)))
    y(q1(b(x1))) -> q2(y(y(x1)))
    y(q2(a(x1))) -> q2(y(a(x1)))
    y(q2(y(x1))) -> q2(y(y(x1)))
    q0(y(x1)) -> y(q3(x1))
    q3(y(x1)) -> y(q3(x1))
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [q3](x0) = x0,
     
     [q2](x0) = 8x0,
     
     [b](x0) = 12x0,
     
     [y](x0) = 2x0,
     
     [q1](x0) = 6x0,
     
     [q0](x0) = x0,
     
     [a](x0) = 4x0
    orientation:
     q1(a(x1)) = 10x1 >= 10x1 = a(q1(x1))
     
     q1(y(x1)) = 8x1 >= 8x1 = y(q1(x1))
     
     a(q1(b(x1))) = 22x1 >= 14x1 = q2(a(y(x1)))
     
     a(q2(a(x1))) = 16x1 >= 16x1 = q2(a(a(x1)))
     
     a(q2(y(x1))) = 14x1 >= 14x1 = q2(a(y(x1)))
     
     y(q1(b(x1))) = 20x1 >= 12x1 = q2(y(y(x1)))
     
     y(q2(a(x1))) = 14x1 >= 14x1 = q2(y(a(x1)))
     
     y(q2(y(x1))) = 12x1 >= 12x1 = q2(y(y(x1)))
     
     q0(y(x1)) = 2x1 >= 2x1 = y(q3(x1))
     
     q3(y(x1)) = 2x1 >= 2x1 = y(q3(x1))
    problem:
     q1(a(x1)) -> a(q1(x1))
     q1(y(x1)) -> y(q1(x1))
     a(q2(a(x1))) -> q2(a(a(x1)))
     a(q2(y(x1))) -> q2(a(y(x1)))
     y(q2(a(x1))) -> q2(y(a(x1)))
     y(q2(y(x1))) -> q2(y(y(x1)))
     q0(y(x1)) -> y(q3(x1))
     q3(y(x1)) -> y(q3(x1))
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [q3](x0) = 8x0,
      
      [q2](x0) = x0,
      
      [y](x0) = 12x0,
      
      [q1](x0) = 12x0,
      
      [q0](x0) = 10x0,
      
      [a](x0) = x0
     orientation:
      q1(a(x1)) = 12x1 >= 12x1 = a(q1(x1))
      
      q1(y(x1)) = 24x1 >= 24x1 = y(q1(x1))
      
      a(q2(a(x1))) = x1 >= x1 = q2(a(a(x1)))
      
      a(q2(y(x1))) = 12x1 >= 12x1 = q2(a(y(x1)))
      
      y(q2(a(x1))) = 12x1 >= 12x1 = q2(y(a(x1)))
      
      y(q2(y(x1))) = 24x1 >= 24x1 = q2(y(y(x1)))
      
      q0(y(x1)) = 22x1 >= 20x1 = y(q3(x1))
      
      q3(y(x1)) = 20x1 >= 20x1 = y(q3(x1))
     problem:
      q1(a(x1)) -> a(q1(x1))
      q1(y(x1)) -> y(q1(x1))
      a(q2(a(x1))) -> q2(a(a(x1)))
      a(q2(y(x1))) -> q2(a(y(x1)))
      y(q2(a(x1))) -> q2(y(a(x1)))
      y(q2(y(x1))) -> q2(y(y(x1)))
      q3(y(x1)) -> y(q3(x1))
     KBO Processor:
      weight function:
       w0 = 1
       w(q3) = w(q2) = w(y) = w(q1) = w(a) = 1
      precedence:
       q1 > q3 > y ~ a > q2
      problem:
       
      Qed