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:
                [0 0]     [0]
      [b](x0) = [0 0]x0 + [0],
      
      [b#](x0) = [0 0]x0 + [0],
      
                [0 0]     [0]
      [a](x0) = [1 0]x0 + [0],
      
      [a#](x0) = [1 0]x0 + [0]
     orientation:
      a#(x1) = [1 0]x1 + [0] >= [0 0]x1 + [0] = b#(x1)
      
      b#(b(a(b(x1)))) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(b(x1))
      
      b#(b(a(b(x1)))) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(b(b(x1)))
      
      b#(b(a(b(x1)))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a#(b(b(b(x1))))
      
      b#(b(a(b(x1)))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a#(a(b(b(b(x1)))))
      
              [0 0]     [0]    [0 0]     [0]        
      a(x1) = [1 0]x1 + [0] >= [0 0]x1 + [0] = b(x1)
      
                       [1 1]     [1]    [1 1]     [1]                    
      b(b(a(b(x1)))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a(a(b(b(b(x1)))))
     problem:
      DPs:
       a#(x1) -> 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)))))
     Restore Modifier:
      DPs:
       a#(x1) -> 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)))))
      EDG Processor:
       DPs:
        a#(x1) -> 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)))) -> 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#(b(b(b(x1))))
        a#(x1) -> b#(x1) -> b#(b(a(b(x1)))) -> a#(a(b(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:
                   [0 0]     [0]
         [b](x0) = [0 0]x0 + [0],
         
         [b#](x0) = [-& 1 ]x0 + [0],
         
                   [0 1]     [0]
         [a](x0) = [0 0]x0 + [0],
         
         [a#](x0) = [-& 2 ]x0 + [2]
        orientation:
         a#(x1) = [-& 2 ]x1 + [2] >= [-& 1 ]x1 + [0] = b#(x1)
         
         b#(b(a(b(x1)))) = [2 2]x1 + [2] >= [2 2]x1 + [2] = a#(b(b(b(x1))))
         
         b#(b(a(b(x1)))) = [2 2]x1 + [2] >= [2 2]x1 + [2] = a#(a(b(b(b(x1)))))
         
                 [0 1]     [0]    [0 0]     [0]        
         a(x1) = [0 0]x1 + [0] >= [0 0]x1 + [0] = b(x1)
         
                          [1 1]     [1]    [1 1]     [1]                    
         b(b(a(b(x1)))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a(a(b(b(b(x1)))))
        problem:
         DPs:
          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)))))
        Restore Modifier:
         DPs:
          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)))))
         EDG Processor:
          DPs:
           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:
           
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 0/4