YES

Problem:
 a(l(x1)) -> l(a(x1))
 r(a(a(x1))) -> a(a(r(x1)))
 b(l(x1)) -> b(a(r(x1)))
 r(b(x1)) -> l(b(x1))

Proof:
 DP Processor:
  DPs:
   a#(l(x1)) -> a#(x1)
   r#(a(a(x1))) -> r#(x1)
   r#(a(a(x1))) -> a#(r(x1))
   r#(a(a(x1))) -> a#(a(r(x1)))
   b#(l(x1)) -> r#(x1)
   b#(l(x1)) -> a#(r(x1))
   b#(l(x1)) -> b#(a(r(x1)))
  TRS:
   a(l(x1)) -> l(a(x1))
   r(a(a(x1))) -> a(a(r(x1)))
   b(l(x1)) -> b(a(r(x1)))
   r(b(x1)) -> l(b(x1))
  TDG Processor:
   DPs:
    a#(l(x1)) -> a#(x1)
    r#(a(a(x1))) -> r#(x1)
    r#(a(a(x1))) -> a#(r(x1))
    r#(a(a(x1))) -> a#(a(r(x1)))
    b#(l(x1)) -> r#(x1)
    b#(l(x1)) -> a#(r(x1))
    b#(l(x1)) -> b#(a(r(x1)))
   TRS:
    a(l(x1)) -> l(a(x1))
    r(a(a(x1))) -> a(a(r(x1)))
    b(l(x1)) -> b(a(r(x1)))
    r(b(x1)) -> l(b(x1))
   graph:
    b#(l(x1)) -> b#(a(r(x1))) -> b#(l(x1)) -> b#(a(r(x1)))
    b#(l(x1)) -> b#(a(r(x1))) -> b#(l(x1)) -> a#(r(x1))
    b#(l(x1)) -> b#(a(r(x1))) -> b#(l(x1)) -> r#(x1)
    b#(l(x1)) -> r#(x1) -> r#(a(a(x1))) -> a#(a(r(x1)))
    b#(l(x1)) -> r#(x1) -> r#(a(a(x1))) -> a#(r(x1))
    b#(l(x1)) -> r#(x1) -> r#(a(a(x1))) -> r#(x1)
    b#(l(x1)) -> a#(r(x1)) -> a#(l(x1)) -> a#(x1)
    r#(a(a(x1))) -> r#(x1) -> r#(a(a(x1))) -> a#(a(r(x1)))
    r#(a(a(x1))) -> r#(x1) -> r#(a(a(x1))) -> a#(r(x1))
    r#(a(a(x1))) -> r#(x1) -> r#(a(a(x1))) -> r#(x1)
    r#(a(a(x1))) -> a#(r(x1)) -> a#(l(x1)) -> a#(x1)
    r#(a(a(x1))) -> a#(a(r(x1))) -> a#(l(x1)) -> a#(x1)
    a#(l(x1)) -> a#(x1) -> a#(l(x1)) -> a#(x1)
   CDG Processor:
    DPs:
     a#(l(x1)) -> a#(x1)
     r#(a(a(x1))) -> r#(x1)
     r#(a(a(x1))) -> a#(r(x1))
     r#(a(a(x1))) -> a#(a(r(x1)))
     b#(l(x1)) -> r#(x1)
     b#(l(x1)) -> a#(r(x1))
     b#(l(x1)) -> b#(a(r(x1)))
    TRS:
     a(l(x1)) -> l(a(x1))
     r(a(a(x1))) -> a(a(r(x1)))
     b(l(x1)) -> b(a(r(x1)))
     r(b(x1)) -> l(b(x1))
    graph:
     b#(l(x1)) -> b#(a(r(x1))) -> b#(l(x1)) -> r#(x1)
     b#(l(x1)) -> b#(a(r(x1))) -> b#(l(x1)) -> a#(r(x1))
     b#(l(x1)) -> b#(a(r(x1))) -> b#(l(x1)) -> b#(a(r(x1)))
     b#(l(x1)) -> a#(r(x1)) -> a#(l(x1)) -> a#(x1)
     r#(a(a(x1))) -> a#(r(x1)) -> a#(l(x1)) -> a#(x1)
     r#(a(a(x1))) -> a#(a(r(x1))) -> a#(l(x1)) -> a#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 6/49
     DPs:
      b#(l(x1)) -> b#(a(r(x1)))
     TRS:
      a(l(x1)) -> l(a(x1))
      r(a(a(x1))) -> a(a(r(x1)))
      b(l(x1)) -> b(a(r(x1)))
      r(b(x1)) -> l(b(x1))
     Matrix Interpretation Processor: dim=4
      
      interpretation:
       [b#](x0) = [0 1 1 0]x0,
       
                 [1]
                 [0]
       [b](x0) = [0]
                 [1],
       
                 [0 0 1 0]  
                 [1 0 0 0]  
       [r](x0) = [1 0 0 0]x0
                 [0 0 1 1]  ,
       
                 [0 1 0 0]  
                 [1 0 0 0]  
       [a](x0) = [0 0 1 0]x0
                 [0 1 0 0]  ,
       
                 [0 1 0 0]     [0]
                 [1 0 0 0]     [0]
       [l](x0) = [0 0 1 0]x0 + [1]
                 [0 0 0 0]     [0]
      orientation:
       b#(l(x1)) = [1 0 1 0]x1 + [1] >= [1 0 1 0]x1 = b#(a(r(x1)))
       
                  [1 0 0 0]     [0]    [1 0 0 0]     [0]           
                  [0 1 0 0]     [0]    [0 1 0 0]     [0]           
       a(l(x1)) = [0 0 1 0]x1 + [1] >= [0 0 1 0]x1 + [1] = l(a(x1))
                  [1 0 0 0]     [0]    [0 0 0 0]     [0]           
       
                     [0 0 1 0]      [0 0 1 0]                
                     [1 0 0 0]      [1 0 0 0]                
       r(a(a(x1))) = [1 0 0 0]x1 >= [1 0 0 0]x1 = a(a(r(x1)))
                     [1 0 1 0]      [0 0 1 0]                
       
                  [1]    [1]              
                  [0]    [0]              
       b(l(x1)) = [0] >= [0] = b(a(r(x1)))
                  [1]    [1]              
       
                  [0]    [0]           
                  [1]    [1]           
       r(b(x1)) = [1] >= [1] = l(b(x1))
                  [1]    [0]           
      problem:
       DPs:
        
       TRS:
        a(l(x1)) -> l(a(x1))
        r(a(a(x1))) -> a(a(r(x1)))
        b(l(x1)) -> b(a(r(x1)))
        r(b(x1)) -> l(b(x1))
      Qed