YES

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

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