YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(a(x1))) -> a#(a(x1))
   a#(b(a(x1))) -> b#(a(a(x1)))
   a#(b(a(x1))) -> b#(b(a(a(x1))))
   a#(b(a(x1))) -> a#(b(b(a(a(x1)))))
   a#(b(a(x1))) -> a#(a(b(b(a(a(x1))))))
   b#(a(a(b(x1)))) -> b#(a(b(x1)))
  TRS:
   a(b(a(x1))) -> a(a(b(b(a(a(x1))))))
   b(a(a(b(x1)))) -> b(a(b(x1)))
  TDG Processor:
   DPs:
    a#(b(a(x1))) -> a#(a(x1))
    a#(b(a(x1))) -> b#(a(a(x1)))
    a#(b(a(x1))) -> b#(b(a(a(x1))))
    a#(b(a(x1))) -> a#(b(b(a(a(x1)))))
    a#(b(a(x1))) -> a#(a(b(b(a(a(x1))))))
    b#(a(a(b(x1)))) -> b#(a(b(x1)))
   TRS:
    a(b(a(x1))) -> a(a(b(b(a(a(x1))))))
    b(a(a(b(x1)))) -> b(a(b(x1)))
   graph:
    b#(a(a(b(x1)))) -> b#(a(b(x1))) ->
    b#(a(a(b(x1)))) -> b#(a(b(x1)))
    a#(b(a(x1))) -> b#(b(a(a(x1)))) -> b#(a(a(b(x1)))) -> b#(a(b(x1)))
    a#(b(a(x1))) -> b#(a(a(x1))) ->
    b#(a(a(b(x1)))) -> b#(a(b(x1)))
    a#(b(a(x1))) -> a#(b(b(a(a(x1))))) ->
    a#(b(a(x1))) -> a#(a(b(b(a(a(x1))))))
    a#(b(a(x1))) -> a#(b(b(a(a(x1))))) ->
    a#(b(a(x1))) -> a#(b(b(a(a(x1)))))
    a#(b(a(x1))) -> a#(b(b(a(a(x1))))) ->
    a#(b(a(x1))) -> b#(b(a(a(x1))))
    a#(b(a(x1))) -> a#(b(b(a(a(x1))))) ->
    a#(b(a(x1))) -> b#(a(a(x1)))
    a#(b(a(x1))) -> a#(b(b(a(a(x1))))) ->
    a#(b(a(x1))) -> a#(a(x1))
    a#(b(a(x1))) -> a#(a(b(b(a(a(x1)))))) ->
    a#(b(a(x1))) -> a#(a(b(b(a(a(x1))))))
    a#(b(a(x1))) -> a#(a(b(b(a(a(x1)))))) ->
    a#(b(a(x1))) -> a#(b(b(a(a(x1)))))
    a#(b(a(x1))) -> a#(a(b(b(a(a(x1)))))) ->
    a#(b(a(x1))) -> b#(b(a(a(x1))))
    a#(b(a(x1))) -> a#(a(b(b(a(a(x1)))))) ->
    a#(b(a(x1))) -> b#(a(a(x1)))
    a#(b(a(x1))) -> a#(a(b(b(a(a(x1)))))) -> a#(b(a(x1))) -> a#(a(x1))
    a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) -> a#(a(b(b(a(a(x1))))))
    a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) -> a#(b(b(a(a(x1)))))
    a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) -> b#(b(a(a(x1))))
    a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) -> b#(a(a(x1)))
    a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1))
   CDG Processor:
    DPs:
     a#(b(a(x1))) -> a#(a(x1))
     a#(b(a(x1))) -> b#(a(a(x1)))
     a#(b(a(x1))) -> b#(b(a(a(x1))))
     a#(b(a(x1))) -> a#(b(b(a(a(x1)))))
     a#(b(a(x1))) -> a#(a(b(b(a(a(x1))))))
     b#(a(a(b(x1)))) -> b#(a(b(x1)))
    TRS:
     a(b(a(x1))) -> a(a(b(b(a(a(x1))))))
     b(a(a(b(x1)))) -> b(a(b(x1)))
    graph:
     b#(a(a(b(x1)))) -> b#(a(b(x1))) -> b#(a(a(b(x1)))) -> b#(a(b(x1)))
     a#(b(a(x1))) -> b#(a(a(x1))) -> b#(a(a(b(x1)))) -> b#(a(b(x1)))
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 2/36
     DPs:
      b#(a(a(b(x1)))) -> b#(a(b(x1)))
     TRS:
      a(b(a(x1))) -> a(a(b(b(a(a(x1))))))
      b(a(a(b(x1)))) -> b(a(b(x1)))
     Matrix Interpretation Processor: dim=4
      
      interpretation:
       [b#](x0) = [1 0 0 0]x0,
       
                 [0 1 0 0]  
                 [0 0 0 0]  
       [b](x0) = [0 0 0 0]x0
                 [1 0 0 0]  ,
       
                 [1 1 0 0]     [0]
                 [0 0 0 0]     [1]
       [a](x0) = [0 0 0 1]x0 + [0]
                 [1 0 1 0]     [0]
      orientation:
       b#(a(a(b(x1)))) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 = b#(a(b(x1)))
       
                     [0 0 0 0]     [1]    [1]                       
                     [0 0 0 0]     [1]    [1]                       
       a(b(a(x1))) = [1 1 0 0]x1 + [0] >= [0] = a(a(b(b(a(a(x1))))))
                     [0 0 0 0]     [1]    [1]                       
       
                        [0 0 0 0]     [1]    [0 0 0 0]     [1]              
                        [0 0 0 0]     [0]    [0 0 0 0]     [0]              
       b(a(a(b(x1)))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = b(a(b(x1)))
                        [0 1 0 0]     [1]    [0 1 0 0]     [0]              
      problem:
       DPs:
        
       TRS:
        a(b(a(x1))) -> a(a(b(b(a(a(x1))))))
        b(a(a(b(x1)))) -> b(a(b(x1)))
      Qed