YES

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

Proof:
 String Reversal Processor:
  b(b(x1)) -> a(a(a(x1)))
  b(a(a(x1))) -> b(x1)
  a(b(a(x1))) -> b(b(a(x1)))
  DP Processor:
   DPs:
    b#(b(x1)) -> a#(x1)
    b#(b(x1)) -> a#(a(x1))
    b#(b(x1)) -> a#(a(a(x1)))
    b#(a(a(x1))) -> b#(x1)
    a#(b(a(x1))) -> b#(b(a(x1)))
   TRS:
    b(b(x1)) -> a(a(a(x1)))
    b(a(a(x1))) -> b(x1)
    a(b(a(x1))) -> b(b(a(x1)))
   TDG Processor:
    DPs:
     b#(b(x1)) -> a#(x1)
     b#(b(x1)) -> a#(a(x1))
     b#(b(x1)) -> a#(a(a(x1)))
     b#(a(a(x1))) -> b#(x1)
     a#(b(a(x1))) -> b#(b(a(x1)))
    TRS:
     b(b(x1)) -> a(a(a(x1)))
     b(a(a(x1))) -> b(x1)
     a(b(a(x1))) -> b(b(a(x1)))
    graph:
     a#(b(a(x1))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> b#(x1)
     a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(a(a(x1)))
     a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(a(x1))
     a#(b(a(x1))) -> b#(b(a(x1))) -> b#(b(x1)) -> a#(x1)
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
     b#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(a(a(x1)))
     b#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(a(x1))
     b#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(x1)
     b#(b(x1)) -> a#(a(a(x1))) -> a#(b(a(x1))) -> b#(b(a(x1)))
     b#(b(x1)) -> a#(a(x1)) -> a#(b(a(x1))) -> b#(b(a(x1)))
     b#(b(x1)) -> a#(x1) -> a#(b(a(x1))) -> b#(b(a(x1)))
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      b(b(x1)) -> a(a(a(x1)))
      b(a(a(x1))) -> b(x1)
      a(b(a(x1))) -> b(b(a(x1)))
     interpretation:
                [0 0]  
      [a](x0) = [0 0]x0,
      
      [a#](x0) = [0 0]x0,
      
                [0 0]  
      [b](x0) = [1 0]x0,
      
      [b#](x0) = [0  -&]x0
     orientation:
      b#(b(x1)) = [0 0]x1 >= [0 0]x1 = a#(x1)
      
      b#(b(x1)) = [0 0]x1 >= [0 0]x1 = a#(a(x1))
      
      b#(b(x1)) = [0 0]x1 >= [0 0]x1 = a#(a(a(x1)))
      
      b#(a(a(x1))) = [0 0]x1 >= [0  -&]x1 = b#(x1)
      
      a#(b(a(x1))) = [1 1]x1 >= [0 0]x1 = b#(b(a(x1)))
      
                 [1 0]      [0 0]                
      b(b(x1)) = [1 1]x1 >= [0 0]x1 = a(a(a(x1)))
      
                    [0 0]      [0 0]          
      b(a(a(x1))) = [1 1]x1 >= [1 0]x1 = b(x1)
      
                    [1 1]      [1 1]                
      a(b(a(x1))) = [1 1]x1 >= [1 1]x1 = b(b(a(x1)))
     problem:
      DPs:
       b#(b(x1)) -> a#(x1)
       b#(b(x1)) -> a#(a(x1))
       b#(b(x1)) -> a#(a(a(x1)))
       b#(a(a(x1))) -> b#(x1)
      TRS:
       b(b(x1)) -> a(a(a(x1)))
       b(a(a(x1))) -> b(x1)
       a(b(a(x1))) -> b(b(a(x1)))
     Restore Modifier:
      DPs:
       b#(b(x1)) -> a#(x1)
       b#(b(x1)) -> a#(a(x1))
       b#(b(x1)) -> a#(a(a(x1)))
       b#(a(a(x1))) -> b#(x1)
      TRS:
       b(b(x1)) -> a(a(a(x1)))
       b(a(a(x1))) -> b(x1)
       a(b(a(x1))) -> b(b(a(x1)))
      EDG Processor:
       DPs:
        b#(b(x1)) -> a#(x1)
        b#(b(x1)) -> a#(a(x1))
        b#(b(x1)) -> a#(a(a(x1)))
        b#(a(a(x1))) -> b#(x1)
       TRS:
        b(b(x1)) -> a(a(a(x1)))
        b(a(a(x1))) -> b(x1)
        a(b(a(x1))) -> b(b(a(x1)))
       graph:
        b#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(x1)
        b#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(a(x1))
        b#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(a(a(x1)))
        b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
       SCC Processor:
        #sccs: 1
        #rules: 1
        #arcs: 4/16
        DPs:
         b#(a(a(x1))) -> b#(x1)
        TRS:
         b(b(x1)) -> a(a(a(x1)))
         b(a(a(x1))) -> b(x1)
         a(b(a(x1))) -> b(b(a(x1)))
        Usable Rule Processor:
         DPs:
          b#(a(a(x1))) -> b#(x1)
         TRS:
          
         Arctic Interpretation Processor:
          dimension: 1
          usable rules:
           
          interpretation:
           [a](x0) = 8x0 + 0,
           
           [b#](x0) = 8x0 + 0
          orientation:
           b#(a(a(x1))) = 24x1 + 16 >= 8x1 + 0 = b#(x1)
          problem:
           DPs:
            
           TRS:
            
          Qed