YES

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

Proof:
 String Reversal Processor:
  b(a(a(x1))) -> a(a(a(b(x1))))
  a(b(a(b(x1)))) -> b(b(a(x1)))
  DP Processor:
   DPs:
    b#(a(a(x1))) -> b#(x1)
    b#(a(a(x1))) -> a#(b(x1))
    b#(a(a(x1))) -> a#(a(b(x1)))
    b#(a(a(x1))) -> a#(a(a(b(x1))))
    a#(b(a(b(x1)))) -> a#(x1)
    a#(b(a(b(x1)))) -> b#(a(x1))
    a#(b(a(b(x1)))) -> b#(b(a(x1)))
   TRS:
    b(a(a(x1))) -> a(a(a(b(x1))))
    a(b(a(b(x1)))) -> b(b(a(x1)))
   TDG Processor:
    DPs:
     b#(a(a(x1))) -> b#(x1)
     b#(a(a(x1))) -> a#(b(x1))
     b#(a(a(x1))) -> a#(a(b(x1)))
     b#(a(a(x1))) -> a#(a(a(b(x1))))
     a#(b(a(b(x1)))) -> a#(x1)
     a#(b(a(b(x1)))) -> b#(a(x1))
     a#(b(a(b(x1)))) -> b#(b(a(x1)))
    TRS:
     b(a(a(x1))) -> a(a(a(b(x1))))
     a(b(a(b(x1)))) -> b(b(a(x1)))
    graph:
     a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> b#(b(a(x1)))
     a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> b#(a(x1))
     a#(b(a(b(x1)))) -> a#(x1) -> a#(b(a(b(x1)))) -> a#(x1)
     a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
     a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(a(b(x1)))
     a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(x1))
     a#(b(a(b(x1)))) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(x1)
     a#(b(a(b(x1)))) -> b#(b(a(x1))) ->
     b#(a(a(x1))) -> a#(a(a(b(x1))))
     a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> a#(a(b(x1)))
     a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> a#(b(x1))
     a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> b#(x1)
     b#(a(a(x1))) -> a#(a(a(b(x1)))) ->
     a#(b(a(b(x1)))) -> b#(b(a(x1)))
     b#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(b(a(b(x1)))) -> b#(a(x1))
     b#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(b(a(b(x1)))) -> a#(x1)
     b#(a(a(x1))) -> a#(a(b(x1))) -> a#(b(a(b(x1)))) -> b#(b(a(x1)))
     b#(a(a(x1))) -> a#(a(b(x1))) -> a#(b(a(b(x1)))) -> b#(a(x1))
     b#(a(a(x1))) -> a#(a(b(x1))) -> a#(b(a(b(x1)))) -> a#(x1)
     b#(a(a(x1))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(b(a(x1)))
     b#(a(a(x1))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(a(x1))
     b#(a(a(x1))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> a#(x1)
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(x1)))
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(x1))
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [a#](x0) = 2x0,
      
      [b#](x0) = 3x0,
      
      [a](x0) = x0,
      
      [b](x0) = 1x0
     orientation:
      b#(a(a(x1))) = 3x1 >= 3x1 = b#(x1)
      
      b#(a(a(x1))) = 3x1 >= 3x1 = a#(b(x1))
      
      b#(a(a(x1))) = 3x1 >= 3x1 = a#(a(b(x1)))
      
      b#(a(a(x1))) = 3x1 >= 3x1 = a#(a(a(b(x1))))
      
      a#(b(a(b(x1)))) = 4x1 >= 2x1 = a#(x1)
      
      a#(b(a(b(x1)))) = 4x1 >= 3x1 = b#(a(x1))
      
      a#(b(a(b(x1)))) = 4x1 >= 4x1 = b#(b(a(x1)))
      
      b(a(a(x1))) = 1x1 >= 1x1 = a(a(a(b(x1))))
      
      a(b(a(b(x1)))) = 2x1 >= 2x1 = b(b(a(x1)))
     problem:
      DPs:
       b#(a(a(x1))) -> b#(x1)
       b#(a(a(x1))) -> a#(b(x1))
       b#(a(a(x1))) -> a#(a(b(x1)))
       b#(a(a(x1))) -> a#(a(a(b(x1))))
       a#(b(a(b(x1)))) -> b#(b(a(x1)))
      TRS:
       b(a(a(x1))) -> a(a(a(b(x1))))
       a(b(a(b(x1)))) -> b(b(a(x1)))
     EDG Processor:
      DPs:
       b#(a(a(x1))) -> b#(x1)
       b#(a(a(x1))) -> a#(b(x1))
       b#(a(a(x1))) -> a#(a(b(x1)))
       b#(a(a(x1))) -> a#(a(a(b(x1))))
       a#(b(a(b(x1)))) -> b#(b(a(x1)))
      TRS:
       b(a(a(x1))) -> a(a(a(b(x1))))
       a(b(a(b(x1)))) -> b(b(a(x1)))
      graph:
       a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> b#(x1)
       a#(b(a(b(x1)))) -> b#(b(a(x1))) -> b#(a(a(x1))) -> a#(b(x1))
       a#(b(a(b(x1)))) -> b#(b(a(x1))) ->
       b#(a(a(x1))) -> a#(a(b(x1)))
       a#(b(a(b(x1)))) -> b#(b(a(x1))) ->
       b#(a(a(x1))) -> a#(a(a(b(x1))))
       b#(a(a(x1))) -> a#(a(a(b(x1)))) ->
       a#(b(a(b(x1)))) -> b#(b(a(x1)))
       b#(a(a(x1))) -> a#(a(b(x1))) -> a#(b(a(b(x1)))) -> b#(b(a(x1)))
       b#(a(a(x1))) -> a#(b(x1)) -> a#(b(a(b(x1)))) -> b#(b(a(x1)))
       b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
       b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(x1))
       b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(x1)))
       b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(b(x1))))
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [a#](x0) = 2x0 + 6,
        
        [b#](x0) = 3x0 + 4,
        
        [a](x0) = x0 + 11/2,
        
        [b](x0) = 3/2x0 + 7/2
       orientation:
        b#(a(a(x1))) = 3x1 + 37 >= 3x1 + 4 = b#(x1)
        
        b#(a(a(x1))) = 3x1 + 37 >= 3x1 + 13 = a#(b(x1))
        
        b#(a(a(x1))) = 3x1 + 37 >= 3x1 + 24 = a#(a(b(x1)))
        
        b#(a(a(x1))) = 3x1 + 37 >= 3x1 + 35 = a#(a(a(b(x1))))
        
        a#(b(a(b(x1)))) = 9/2x1 + 40 >= 9/2x1 + 157/4 = b#(b(a(x1)))
        
        b(a(a(x1))) = 3/2x1 + 20 >= 3/2x1 + 20 = a(a(a(b(x1))))
        
        a(b(a(b(x1)))) = 9/4x1 + 45/2 >= 9/4x1 + 169/8 = b(b(a(x1)))
       problem:
        DPs:
         
        TRS:
         b(a(a(x1))) -> a(a(a(b(x1))))
         a(b(a(b(x1)))) -> b(b(a(x1)))
       Qed