YES

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

Proof:
 String Reversal Processor:
  b(b(a(a(x1)))) -> a(a(b(a(x1))))
  a(x1) -> b(b(b(x1)))
  DP Processor:
   DPs:
    b#(b(a(a(x1)))) -> b#(a(x1))
    b#(b(a(a(x1)))) -> a#(b(a(x1)))
    b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
    a#(x1) -> b#(x1)
    a#(x1) -> b#(b(x1))
    a#(x1) -> b#(b(b(x1)))
   TRS:
    b(b(a(a(x1)))) -> a(a(b(a(x1))))
    a(x1) -> b(b(b(x1)))
   TDG Processor:
    DPs:
     b#(b(a(a(x1)))) -> b#(a(x1))
     b#(b(a(a(x1)))) -> a#(b(a(x1)))
     b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
     a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1))
     a#(x1) -> b#(b(b(x1)))
    TRS:
     b(b(a(a(x1)))) -> a(a(b(a(x1))))
     a(x1) -> b(b(b(x1)))
    graph:
     a#(x1) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
     a#(x1) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> a#(b(a(x1)))
     a#(x1) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(a(x1))
     a#(x1) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
     a#(x1) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(b(a(x1)))
     a#(x1) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(a(x1))
     a#(x1) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
     a#(x1) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(b(a(x1)))
     a#(x1) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(a(x1))
     b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> a#(x1) -> b#(b(b(x1)))
     b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> a#(x1) -> b#(b(x1))
     b#(b(a(a(x1)))) -> a#(a(b(a(x1)))) -> a#(x1) -> b#(x1)
     b#(b(a(a(x1)))) -> a#(b(a(x1))) -> a#(x1) -> b#(b(b(x1)))
     b#(b(a(a(x1)))) -> a#(b(a(x1))) -> a#(x1) -> b#(b(x1))
     b#(b(a(a(x1)))) -> a#(b(a(x1))) -> a#(x1) -> b#(x1)
     b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> a#(a(b(a(x1))))
     b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> a#(b(a(x1)))
     b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> b#(a(x1))
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      b(b(a(a(x1)))) -> a(a(b(a(x1))))
      a(x1) -> b(b(b(x1)))
     interpretation:
                [1  0 ]     [1]
      [a](x0) = [0  -&]x0 + [0],
      
      [a#](x0) = [0 0]x0 + [0],
      
                [-& 0 ]     [0]
      [b](x0) = [0  -&]x0 + [0],
      
      [b#](x0) = [-& 0 ]x0 + [0]
     orientation:
      b#(b(a(a(x1)))) = [2 1]x1 + [2] >= [0  -&]x1 + [0] = b#(a(x1))
      
      b#(b(a(a(x1)))) = [2 1]x1 + [2] >= [1 0]x1 + [1] = a#(b(a(x1)))
      
      b#(b(a(a(x1)))) = [2 1]x1 + [2] >= [1 0]x1 + [1] = a#(a(b(a(x1))))
      
      a#(x1) = [0 0]x1 + [0] >= [-& 0 ]x1 + [0] = b#(x1)
      
      a#(x1) = [0 0]x1 + [0] >= [0  -&]x1 + [0] = b#(b(x1))
      
      a#(x1) = [0 0]x1 + [0] >= [-& 0 ]x1 + [0] = b#(b(b(x1)))
      
                       [2 1]     [2]    [2 1]     [2]                 
      b(b(a(a(x1)))) = [1 0]x1 + [1] >= [1 0]x1 + [1] = a(a(b(a(x1))))
      
              [1  0 ]     [1]    [-& 0 ]     [0]              
      a(x1) = [0  -&]x1 + [0] >= [0  -&]x1 + [0] = b(b(b(x1)))
     problem:
      DPs:
       a#(x1) -> b#(x1)
       a#(x1) -> b#(b(x1))
       a#(x1) -> b#(b(b(x1)))
      TRS:
       b(b(a(a(x1)))) -> a(a(b(a(x1))))
       a(x1) -> b(b(b(x1)))
     Restore Modifier:
      DPs:
       a#(x1) -> b#(x1)
       a#(x1) -> b#(b(x1))
       a#(x1) -> b#(b(b(x1)))
      TRS:
       b(b(a(a(x1)))) -> a(a(b(a(x1))))
       a(x1) -> b(b(b(x1)))
      EDG Processor:
       DPs:
        a#(x1) -> b#(x1)
        a#(x1) -> b#(b(x1))
        a#(x1) -> b#(b(b(x1)))
       TRS:
        b(b(a(a(x1)))) -> a(a(b(a(x1))))
        a(x1) -> b(b(b(x1)))
       graph:
        
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 0/9