YES

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

Proof:
 String Reversal Processor:
  a(x1) -> b(x1)
  b(b(a(b(x1)))) -> a(a(b(b(b(x1)))))
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    b#(b(a(b(x1)))) -> b#(b(x1))
    b#(b(a(b(x1)))) -> b#(b(b(x1)))
    b#(b(a(b(x1)))) -> a#(b(b(b(x1))))
    b#(b(a(b(x1)))) -> a#(a(b(b(b(x1)))))
   TRS:
    a(x1) -> b(x1)
    b(b(a(b(x1)))) -> a(a(b(b(b(x1)))))
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     b#(b(a(b(x1)))) -> b#(b(x1))
     b#(b(a(b(x1)))) -> b#(b(b(x1)))
     b#(b(a(b(x1)))) -> a#(b(b(b(x1))))
     b#(b(a(b(x1)))) -> a#(a(b(b(b(x1)))))
    TRS:
     a(x1) -> b(x1)
     b(b(a(b(x1)))) -> a(a(b(b(b(x1)))))
    graph:
     b#(b(a(b(x1)))) -> b#(b(b(x1))) ->
     b#(b(a(b(x1)))) -> a#(a(b(b(b(x1)))))
     b#(b(a(b(x1)))) -> b#(b(b(x1))) ->
     b#(b(a(b(x1)))) -> a#(b(b(b(x1))))
     b#(b(a(b(x1)))) -> b#(b(b(x1))) ->
     b#(b(a(b(x1)))) -> b#(b(b(x1)))
     b#(b(a(b(x1)))) -> b#(b(b(x1))) -> b#(b(a(b(x1)))) -> b#(b(x1))
     b#(b(a(b(x1)))) -> b#(b(x1)) ->
     b#(b(a(b(x1)))) -> a#(a(b(b(b(x1)))))
     b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> a#(b(b(b(x1))))
     b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(b(x1)))
     b#(b(a(b(x1)))) -> b#(b(x1)) -> b#(b(a(b(x1)))) -> b#(b(x1))
     b#(b(a(b(x1)))) -> a#(b(b(b(x1)))) -> a#(x1) -> b#(x1)
     b#(b(a(b(x1)))) -> a#(a(b(b(b(x1))))) -> a#(x1) -> b#(x1)
     a#(x1) -> b#(x1) -> b#(b(a(b(x1)))) -> a#(a(b(b(b(x1)))))
     a#(x1) -> b#(x1) -> b#(b(a(b(x1)))) -> a#(b(b(b(x1))))
     a#(x1) -> b#(x1) -> b#(b(a(b(x1)))) -> b#(b(b(x1)))
     a#(x1) -> b#(x1) -> b#(b(a(b(x1)))) -> b#(b(x1))
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> b(x1)
      b(b(a(b(x1)))) -> a(a(b(b(b(x1)))))
     interpretation:
      [b#](x0) = [0 2]x0,
      
      [a#](x0) = [0 3]x0 + [0],
      
                [-& 0 ]     [0]
      [b](x0) = [0  0 ]x0 + [0],
      
                [-& 2 ]     [3]
      [a](x0) = [0  0 ]x0 + [1]
     orientation:
      a#(x1) = [0 3]x1 + [0] >= [0 2]x1 = b#(x1)
      
      b#(b(a(b(x1)))) = [4 4]x1 + [5] >= [2 2]x1 + [2] = b#(b(x1))
      
      b#(b(a(b(x1)))) = [4 4]x1 + [5] >= [2 2]x1 + [2] = b#(b(b(x1)))
      
      b#(b(a(b(x1)))) = [4 4]x1 + [5] >= [3 3]x1 + [3] = a#(b(b(b(x1))))
      
      b#(b(a(b(x1)))) = [4 4]x1 + [5] >= [3 3]x1 + [4] = a#(a(b(b(b(x1)))))
      
              [-& 2 ]     [3]    [-& 0 ]     [0]        
      a(x1) = [0  0 ]x1 + [1] >= [0  0 ]x1 + [0] = b(x1)
      
                       [2 2]     [3]    [2 2]     [3]                    
      b(b(a(b(x1)))) = [2 2]x1 + [3] >= [2 2]x1 + [3] = a(a(b(b(b(x1)))))
     problem:
      DPs:
       a#(x1) -> b#(x1)
      TRS:
       a(x1) -> b(x1)
       b(b(a(b(x1)))) -> a(a(b(b(b(x1)))))
     Restore Modifier:
      DPs:
       a#(x1) -> b#(x1)
      TRS:
       a(x1) -> b(x1)
       b(b(a(b(x1)))) -> a(a(b(b(b(x1)))))
      EDG Processor:
       DPs:
        a#(x1) -> b#(x1)
       TRS:
        a(x1) -> b(x1)
        b(b(a(b(x1)))) -> a(a(b(b(b(x1)))))
       graph:
        
       Qed