YES

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

Proof:
 DP Processor:
  DPs:
   b#(b(b(x1))) -> a#(b(x1))
   b#(b(b(x1))) -> b#(a(b(x1)))
   a#(a(x1)) -> b#(x1)
   a#(a(x1)) -> b#(b(x1))
   a#(a(x1)) -> b#(b(b(x1)))
  TRS:
   a(b(a(x1))) -> b(a(x1))
   b(b(b(x1))) -> b(a(b(x1)))
   a(a(x1)) -> b(b(b(x1)))
  TDG Processor:
   DPs:
    b#(b(b(x1))) -> a#(b(x1))
    b#(b(b(x1))) -> b#(a(b(x1)))
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> b#(b(x1))
    a#(a(x1)) -> b#(b(b(x1)))
   TRS:
    a(b(a(x1))) -> b(a(x1))
    b(b(b(x1))) -> b(a(b(x1)))
    a(a(x1)) -> b(b(b(x1)))
   graph:
    b#(b(b(x1))) -> b#(a(b(x1))) -> b#(b(b(x1))) -> b#(a(b(x1)))
    b#(b(b(x1))) -> b#(a(b(x1))) -> b#(b(b(x1))) -> a#(b(x1))
    b#(b(b(x1))) -> a#(b(x1)) -> a#(a(x1)) -> b#(b(b(x1)))
    b#(b(b(x1))) -> a#(b(x1)) -> a#(a(x1)) -> b#(b(x1))
    b#(b(b(x1))) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> b#(b(b(x1))) -> b#(b(b(x1))) -> b#(a(b(x1)))
    a#(a(x1)) -> b#(b(b(x1))) -> b#(b(b(x1))) -> a#(b(x1))
    a#(a(x1)) -> b#(b(x1)) -> b#(b(b(x1))) -> b#(a(b(x1)))
    a#(a(x1)) -> b#(b(x1)) -> b#(b(b(x1))) -> a#(b(x1))
    a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> b#(a(b(x1)))
    a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> a#(b(x1))
   EDG Processor:
    DPs:
     b#(b(b(x1))) -> a#(b(x1))
     b#(b(b(x1))) -> b#(a(b(x1)))
     a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> b#(b(x1))
     a#(a(x1)) -> b#(b(b(x1)))
    TRS:
     a(b(a(x1))) -> b(a(x1))
     b(b(b(x1))) -> b(a(b(x1)))
     a(a(x1)) -> b(b(b(x1)))
    graph:
     b#(b(b(x1))) -> b#(a(b(x1))) -> b#(b(b(x1))) -> a#(b(x1))
     b#(b(b(x1))) -> b#(a(b(x1))) -> b#(b(b(x1))) -> b#(a(b(x1)))
     a#(a(x1)) -> b#(b(b(x1))) -> b#(b(b(x1))) -> a#(b(x1))
     a#(a(x1)) -> b#(b(b(x1))) -> b#(b(b(x1))) -> b#(a(b(x1)))
     a#(a(x1)) -> b#(b(x1)) -> b#(b(b(x1))) -> a#(b(x1))
     a#(a(x1)) -> b#(b(x1)) -> b#(b(b(x1))) -> b#(a(b(x1)))
     a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> a#(b(x1))
     a#(a(x1)) -> b#(x1) -> b#(b(b(x1))) -> b#(a(b(x1)))
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 8/25
     DPs:
      b#(b(b(x1))) -> b#(a(b(x1)))
     TRS:
      a(b(a(x1))) -> b(a(x1))
      b(b(b(x1))) -> b(a(b(x1)))
      a(a(x1)) -> b(b(b(x1)))
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [b#](x0) = [0 0]x0,
       
                 [1  0 ]  
       [b](x0) = [-& -&]x0,
       
                 [0 3]  
       [a](x0) = [0 0]x0
      orientation:
       b#(b(b(x1))) = [2 1]x1 >= [1 0]x1 = b#(a(b(x1)))
       
                     [1 4]      [1  4 ]             
       a(b(a(x1))) = [1 4]x1 >= [-& -&]x1 = b(a(x1))
       
                     [3  2 ]      [2  1 ]                
       b(b(b(x1))) = [-& -&]x1 >= [-& -&]x1 = b(a(b(x1)))
       
                  [3 3]      [3  2 ]                
       a(a(x1)) = [0 3]x1 >= [-& -&]x1 = b(b(b(x1)))
      problem:
       DPs:
        
       TRS:
        a(b(a(x1))) -> b(a(x1))
        b(b(b(x1))) -> b(a(b(x1)))
        a(a(x1)) -> b(b(b(x1)))
      Qed