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)))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
       [b#](x0) = [1 0 0]x0 + [1],
       
                 [1 0 0]     [1]
       [b](x0) = [1 0 0]x0 + [0]
                 [0 0 0]     [0],
       
                 [0 1 1]     [1]
       [a](x0) = [1 0 1]x0 + [1]
                 [1 0 0]     [1]
      orientation:
       b#(b(b(x1))) = [1 0 0]x1 + [3] >= [1 0 0]x1 + [2] = b#(a(b(x1)))
       
                     [0 1 1]     [2]    [0 1 1]     [2]           
       a(b(a(x1))) = [0 1 1]x1 + [3] >= [0 1 1]x1 + [1] = b(a(x1))
                     [0 1 1]     [3]    [0 0 0]     [0]           
       
                     [1 0 0]     [3]    [1 0 0]     [2]              
       b(b(b(x1))) = [1 0 0]x1 + [2] >= [1 0 0]x1 + [1] = b(a(b(x1)))
                     [0 0 0]     [0]    [0 0 0]     [0]              
       
                  [2 0 1]     [3]    [1 0 0]     [3]              
       a(a(x1)) = [1 1 1]x1 + [3] >= [1 0 0]x1 + [2] = b(b(b(x1)))
                  [0 1 1]     [2]    [0 0 0]     [0]              
      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