YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(a(x1))) -> a(b(b(a(x1))))
  b(b(b(x1))) -> a(x1)
  DP Processor:
   DPs:
    b#(a(a(x1))) -> b#(a(x1))
    b#(a(a(x1))) -> b#(b(a(x1)))
    b#(a(a(x1))) -> a#(b(b(a(x1))))
    b#(b(b(x1))) -> a#(x1)
   TRS:
    a(x1) -> x1
    b(a(a(x1))) -> a(b(b(a(x1))))
    b(b(b(x1))) -> a(x1)
   TDG Processor:
    DPs:
     b#(a(a(x1))) -> b#(a(x1))
     b#(a(a(x1))) -> b#(b(a(x1)))
     b#(a(a(x1))) -> a#(b(b(a(x1))))
     b#(b(b(x1))) -> a#(x1)
    TRS:
     a(x1) -> x1
     b(a(a(x1))) -> a(b(b(a(x1))))
     b(b(b(x1))) -> a(x1)
    graph:
     b#(a(a(x1))) -> b#(b(a(x1))) -> b#(b(b(x1))) -> a#(x1)
     b#(a(a(x1))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> a#(b(b(a(x1))))
     b#(a(a(x1))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> b#(b(a(x1)))
     b#(a(a(x1))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> b#(a(x1))
     b#(a(a(x1))) -> b#(a(x1)) -> b#(b(b(x1))) -> a#(x1)
     b#(a(a(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(b(a(x1))))
     b#(a(a(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(b(a(x1)))
     b#(a(a(x1))) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(a(x1))
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 8/16
     DPs:
      b#(a(a(x1))) -> b#(b(a(x1)))
      b#(a(a(x1))) -> b#(a(x1))
     TRS:
      a(x1) -> x1
      b(a(a(x1))) -> a(b(b(a(x1))))
      b(b(b(x1))) -> a(x1)
     Arctic Interpretation Processor:
      dimension: 3
      usable rules:
       a(x1) -> x1
       b(a(a(x1))) -> a(b(b(a(x1))))
       b(b(b(x1))) -> a(x1)
      interpretation:
       [b#](x0) = [-& 0  0 ]x0 + [0],
       
                 [0  0  0 ]     [0]
       [b](x0) = [0  0  -&]x0 + [0]
                 [0  1  0 ]     [0],
       
                 [0  0  0 ]     [0]
       [a](x0) = [0  1  0 ]x0 + [0]
                 [-& 0  0 ]     [0]
      orientation:
       b#(a(a(x1))) = [1 2 1]x1 + [1] >= [1 2 1]x1 + [1] = b#(b(a(x1)))
       
       b#(a(a(x1))) = [1 2 1]x1 + [1] >= [0 1 0]x1 + [0] = b#(a(x1))
       
               [0  0  0 ]     [0]           
       a(x1) = [0  1  0 ]x1 + [0] >= x1 = x1
               [-& 0  0 ]     [0]           
       
                     [1 2 1]     [1]    [1 2 1]     [1]                 
       b(a(a(x1))) = [1 2 1]x1 + [1] >= [1 2 1]x1 + [1] = a(b(b(a(x1))))
                     [2 3 2]     [2]    [1 2 1]     [1]                 
       
                     [1 1 0]     [1]    [0  0  0 ]     [0]        
       b(b(b(x1))) = [0 1 0]x1 + [0] >= [0  1  0 ]x1 + [0] = a(x1)
                     [1 1 1]     [1]    [-& 0  0 ]     [0]        
      problem:
       DPs:
        b#(a(a(x1))) -> b#(b(a(x1)))
       TRS:
        a(x1) -> x1
        b(a(a(x1))) -> a(b(b(a(x1))))
        b(b(b(x1))) -> a(x1)
      Restore Modifier:
       DPs:
        b#(a(a(x1))) -> b#(b(a(x1)))
       TRS:
        a(x1) -> x1
        b(a(a(x1))) -> a(b(b(a(x1))))
        b(b(b(x1))) -> a(x1)
       EDG Processor:
        DPs:
         b#(a(a(x1))) -> b#(b(a(x1)))
        TRS:
         a(x1) -> x1
         b(a(a(x1))) -> a(b(b(a(x1))))
         b(b(b(x1))) -> a(x1)
        graph:
         b#(a(a(x1))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> b#(b(a(x1)))
        Arctic Interpretation Processor:
         dimension: 3
         usable rules:
          a(x1) -> x1
          b(a(a(x1))) -> a(b(b(a(x1))))
          b(b(b(x1))) -> a(x1)
         interpretation:
          [b#](x0) = [0 0 1]x0 + [0],
          
                    [0  0  0 ]     [-&]
          [b](x0) = [1  0  1 ]x0 + [-&]
                    [0  -& 0 ]     [0 ],
          
                    [0  0  -&]     [0]
          [a](x0) = [0  0  -&]x0 + [0]
                    [0  0  1 ]     [0]
         orientation:
          b#(a(a(x1))) = [2 2 3]x1 + [2] >= [1 1 2]x1 + [1] = b#(b(a(x1)))
          
                  [0  0  -&]     [0]           
          a(x1) = [0  0  -&]x1 + [0] >= x1 = x1
                  [0  0  1 ]     [0]           
          
                        [1 1 2]     [1]    [1 1 2]     [1]                 
          b(a(a(x1))) = [2 2 3]x1 + [2] >= [1 1 2]x1 + [1] = a(b(b(a(x1))))
                        [1 1 2]     [1]    [1 1 2]     [1]                 
          
                        [1 1 1]     [1]    [0  0  -&]     [0]        
          b(b(b(x1))) = [2 1 2]x1 + [1] >= [0  0  -&]x1 + [0] = a(x1)
                        [1 0 1]     [0]    [0  0  1 ]     [0]        
         problem:
          DPs:
           
          TRS:
           a(x1) -> x1
           b(a(a(x1))) -> a(b(b(a(x1))))
           b(b(b(x1))) -> a(x1)
         Qed