YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(a(b(x1)))) -> a#(x1)
   a#(a(a(b(x1)))) -> a#(a(x1))
   a#(a(a(b(x1)))) -> a#(a(a(x1)))
   a#(a(a(b(x1)))) -> b#(a(a(a(x1))))
   b#(a(b(a(x1)))) -> b#(b(a(x1)))
   b#(a(b(a(x1)))) -> a#(b(b(a(x1))))
  TRS:
   a(a(a(b(x1)))) -> b(a(a(a(x1))))
   b(a(b(a(x1)))) -> a(b(b(a(x1))))
  TDG Processor:
   DPs:
    a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> a#(a(x1))
    a#(a(a(b(x1)))) -> a#(a(a(x1)))
    a#(a(a(b(x1)))) -> b#(a(a(a(x1))))
    b#(a(b(a(x1)))) -> b#(b(a(x1)))
    b#(a(b(a(x1)))) -> a#(b(b(a(x1))))
   TRS:
    a(a(a(b(x1)))) -> b(a(a(a(x1))))
    b(a(b(a(x1)))) -> a(b(b(a(x1))))
   graph:
    b#(a(b(a(x1)))) -> b#(b(a(x1))) ->
    b#(a(b(a(x1)))) -> a#(b(b(a(x1))))
    b#(a(b(a(x1)))) -> b#(b(a(x1))) ->
    b#(a(b(a(x1)))) -> b#(b(a(x1)))
    b#(a(b(a(x1)))) -> a#(b(b(a(x1)))) ->
    a#(a(a(b(x1)))) -> b#(a(a(a(x1))))
    b#(a(b(a(x1)))) -> a#(b(b(a(x1)))) ->
    a#(a(a(b(x1)))) -> a#(a(a(x1)))
    b#(a(b(a(x1)))) -> a#(b(b(a(x1)))) ->
    a#(a(a(b(x1)))) -> a#(a(x1))
    b#(a(b(a(x1)))) -> a#(b(b(a(x1)))) ->
    a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> b#(a(a(a(x1)))) ->
    b#(a(b(a(x1)))) -> a#(b(b(a(x1))))
    a#(a(a(b(x1)))) -> b#(a(a(a(x1)))) ->
    b#(a(b(a(x1)))) -> b#(b(a(x1)))
    a#(a(a(b(x1)))) -> a#(a(a(x1))) ->
    a#(a(a(b(x1)))) -> b#(a(a(a(x1))))
    a#(a(a(b(x1)))) -> a#(a(a(x1))) ->
    a#(a(a(b(x1)))) -> a#(a(a(x1)))
    a#(a(a(b(x1)))) -> a#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(a(x1))
    a#(a(a(b(x1)))) -> a#(a(a(x1))) -> a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(b(x1)))) -> b#(a(a(a(x1))))
    a#(a(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(b(x1)))) -> a#(a(a(x1)))
    a#(a(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(b(x1)))) -> a#(a(x1))
    a#(a(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> b#(a(a(a(x1))))
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(a(a(x1)))
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(a(x1))
    a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [b#](x0) = 10x0 + 0,
     
     [a#](x0) = x0 + -15,
     
     [a](x0) = 2x0 + -16,
     
     [b](x0) = 12x0 + -4
    orientation:
     a#(a(a(b(x1)))) = 16x1 + 0 >= x1 + -15 = a#(x1)
     
     a#(a(a(b(x1)))) = 16x1 + 0 >= 2x1 + -15 = a#(a(x1))
     
     a#(a(a(b(x1)))) = 16x1 + 0 >= 4x1 + -14 = a#(a(a(x1)))
     
     a#(a(a(b(x1)))) = 16x1 + 0 >= 16x1 + 0 = b#(a(a(a(x1))))
     
     b#(a(b(a(x1)))) = 26x1 + 8 >= 24x1 + 6 = b#(b(a(x1)))
     
     b#(a(b(a(x1)))) = 26x1 + 8 >= 26x1 + 8 = a#(b(b(a(x1))))
     
     a(a(a(b(x1)))) = 18x1 + 2 >= 18x1 + 0 = b(a(a(a(x1))))
     
     b(a(b(a(x1)))) = 28x1 + 10 >= 28x1 + 10 = a(b(b(a(x1))))
    problem:
     DPs:
      a#(a(a(b(x1)))) -> b#(a(a(a(x1))))
      b#(a(b(a(x1)))) -> a#(b(b(a(x1))))
     TRS:
      a(a(a(b(x1)))) -> b(a(a(a(x1))))
      b(a(b(a(x1)))) -> a(b(b(a(x1))))
    EDG Processor:
     DPs:
      a#(a(a(b(x1)))) -> b#(a(a(a(x1))))
      b#(a(b(a(x1)))) -> a#(b(b(a(x1))))
     TRS:
      a(a(a(b(x1)))) -> b(a(a(a(x1))))
      b(a(b(a(x1)))) -> a(b(b(a(x1))))
     graph:
      b#(a(b(a(x1)))) -> a#(b(b(a(x1)))) ->
      a#(a(a(b(x1)))) -> b#(a(a(a(x1))))
      a#(a(a(b(x1)))) -> b#(a(a(a(x1)))) -> b#(a(b(a(x1)))) -> a#(b(b(a(x1))))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
       [b#](x0) = [1 1 0]x0,
       
       [a#](x0) = [1 0 0]x0,
       
                 [0 1 0]  
       [a](x0) = [0 0 1]x0
                 [1 0 0]  ,
       
                 [1 0 0]     [0]
       [b](x0) = [0 1 0]x0 + [0]
                 [1 1 0]     [1]
      orientation:
       a#(a(a(b(x1)))) = [1 1 0]x1 + [1] >= [1 1 0]x1 = b#(a(a(a(x1))))
       
       b#(a(b(a(x1)))) = [0 1 2]x1 + [1] >= [0 1 0]x1 = a#(b(b(a(x1))))
       
                        [1 0 0]     [0]    [1 0 0]     [0]                 
       a(a(a(b(x1)))) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = b(a(a(a(x1))))
                        [1 1 0]     [1]    [1 1 0]     [1]                 
       
                        [0 0 1]     [0]    [0 0 1]     [0]                 
       b(a(b(a(x1)))) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = a(b(b(a(x1))))
                        [0 1 2]     [2]    [0 1 0]     [0]                 
      problem:
       DPs:
        
       TRS:
        a(a(a(b(x1)))) -> b(a(a(a(x1))))
        b(a(b(a(x1)))) -> a(b(b(a(x1))))
      Qed