YES

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

Proof:
 DP Processor:
  DPs:
   b#(a(x1)) -> b#(x1)
   b#(a(x1)) -> a#(b(x1))
   a#(a(a(x1))) -> b#(x1)
   a#(a(a(x1))) -> a#(b(x1))
   a#(a(a(x1))) -> a#(a(b(x1)))
   a#(a(a(x1))) -> b#(a(a(b(x1))))
   b#(b(b(b(x1)))) -> a#(x1)
  TRS:
   b(a(x1)) -> a(b(x1))
   a(a(a(x1))) -> b(a(a(b(x1))))
   b(b(b(b(x1)))) -> a(x1)
  TDG Processor:
   DPs:
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> a#(b(x1))
    a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> a#(b(x1))
    a#(a(a(x1))) -> a#(a(b(x1)))
    a#(a(a(x1))) -> b#(a(a(b(x1))))
    b#(b(b(b(x1)))) -> a#(x1)
   TRS:
    b(a(x1)) -> a(b(x1))
    a(a(a(x1))) -> b(a(a(b(x1))))
    b(b(b(b(x1)))) -> a(x1)
   graph:
    a#(a(a(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(a(a(b(x1))))
    a#(a(a(x1))) -> a#(b(x1)) -> a#(a(a(x1))) -> a#(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))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> b#(a(a(b(x1))))
    a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> a#(a(b(x1)))
    a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> a#(b(x1))
    a#(a(a(x1))) -> a#(a(b(x1))) -> a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> b#(a(a(b(x1)))) -> b#(b(b(b(x1)))) -> a#(x1)
    a#(a(a(x1))) -> b#(a(a(b(x1)))) -> b#(a(x1)) -> a#(b(x1))
    a#(a(a(x1))) -> b#(a(a(b(x1)))) -> b#(a(x1)) -> b#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(b(b(b(x1)))) -> a#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
    a#(a(a(x1))) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    b#(b(b(b(x1)))) -> a#(x1) -> a#(a(a(x1))) -> b#(a(a(b(x1))))
    b#(b(b(b(x1)))) -> a#(x1) -> a#(a(a(x1))) -> a#(a(b(x1)))
    b#(b(b(b(x1)))) -> a#(x1) -> a#(a(a(x1))) -> a#(b(x1))
    b#(b(b(b(x1)))) -> a#(x1) -> a#(a(a(x1))) -> b#(x1)
    b#(a(x1)) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(a(a(b(x1))))
    b#(a(x1)) -> a#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(x1)))
    b#(a(x1)) -> a#(b(x1)) -> a#(a(a(x1))) -> a#(b(x1))
    b#(a(x1)) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(x1)
    b#(a(x1)) -> b#(x1) -> b#(b(b(b(x1)))) -> a#(x1)
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [a#](x0) = 3x0 + 0,
     
     [b#](x0) = 2x0 + 8,
     
     [b](x0) = 1x0 + 2,
     
     [a](x0) = 2x0 + 4
    orientation:
     b#(a(x1)) = 4x1 + 8 >= 2x1 + 8 = b#(x1)
     
     b#(a(x1)) = 4x1 + 8 >= 4x1 + 5 = a#(b(x1))
     
     a#(a(a(x1))) = 7x1 + 9 >= 2x1 + 8 = b#(x1)
     
     a#(a(a(x1))) = 7x1 + 9 >= 4x1 + 5 = a#(b(x1))
     
     a#(a(a(x1))) = 7x1 + 9 >= 6x1 + 7 = a#(a(b(x1)))
     
     a#(a(a(x1))) = 7x1 + 9 >= 7x1 + 8 = b#(a(a(b(x1))))
     
     b#(b(b(b(x1)))) = 5x1 + 8 >= 3x1 + 0 = a#(x1)
     
     b(a(x1)) = 3x1 + 5 >= 3x1 + 4 = a(b(x1))
     
     a(a(a(x1))) = 6x1 + 8 >= 6x1 + 7 = b(a(a(b(x1))))
     
     b(b(b(b(x1)))) = 4x1 + 5 >= 2x1 + 4 = a(x1)
    problem:
     DPs:
      b#(a(x1)) -> b#(x1)
      b#(a(x1)) -> a#(b(x1))
      a#(a(a(x1))) -> b#(a(a(b(x1))))
     TRS:
      b(a(x1)) -> a(b(x1))
      a(a(a(x1))) -> b(a(a(b(x1))))
      b(b(b(b(x1)))) -> a(x1)
    EDG Processor:
     DPs:
      b#(a(x1)) -> b#(x1)
      b#(a(x1)) -> a#(b(x1))
      a#(a(a(x1))) -> b#(a(a(b(x1))))
     TRS:
      b(a(x1)) -> a(b(x1))
      a(a(a(x1))) -> b(a(a(b(x1))))
      b(b(b(b(x1)))) -> a(x1)
     graph:
      a#(a(a(x1))) -> b#(a(a(b(x1)))) -> b#(a(x1)) -> b#(x1)
      a#(a(a(x1))) -> b#(a(a(b(x1)))) -> b#(a(x1)) -> a#(b(x1))
      b#(a(x1)) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(a(a(b(x1))))
      b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
      b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [a#](x0) = 1x0,
       
       [b#](x0) = x0 + 5,
       
       [b](x0) = 1x0 + -2,
       
       [a](x0) = 3x0 + 1
      orientation:
       b#(a(x1)) = 3x1 + 5 >= x1 + 5 = b#(x1)
       
       b#(a(x1)) = 3x1 + 5 >= 2x1 + -1 = a#(b(x1))
       
       a#(a(a(x1))) = 7x1 + 5 >= 7x1 + 5 = b#(a(a(b(x1))))
       
       b(a(x1)) = 4x1 + 2 >= 4x1 + 1 = a(b(x1))
       
       a(a(a(x1))) = 9x1 + 7 >= 8x1 + 5 = b(a(a(b(x1))))
       
       b(b(b(b(x1)))) = 4x1 + 1 >= 3x1 + 1 = a(x1)
      problem:
       DPs:
        b#(a(x1)) -> b#(x1)
        a#(a(a(x1))) -> b#(a(a(b(x1))))
       TRS:
        b(a(x1)) -> a(b(x1))
        a(a(a(x1))) -> b(a(a(b(x1))))
        b(b(b(b(x1)))) -> a(x1)
      EDG Processor:
       DPs:
        b#(a(x1)) -> b#(x1)
        a#(a(a(x1))) -> b#(a(a(b(x1))))
       TRS:
        b(a(x1)) -> a(b(x1))
        a(a(a(x1))) -> b(a(a(b(x1))))
        b(b(b(b(x1)))) -> a(x1)
       graph:
        a#(a(a(x1))) -> b#(a(a(b(x1)))) -> b#(a(x1)) -> b#(x1)
        b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
       CDG Processor:
        DPs:
         b#(a(x1)) -> b#(x1)
         a#(a(a(x1))) -> b#(a(a(b(x1))))
        TRS:
         b(a(x1)) -> a(b(x1))
         a(a(a(x1))) -> b(a(a(b(x1))))
         b(b(b(b(x1)))) -> a(x1)
        graph:
         a#(a(a(x1))) -> b#(a(a(b(x1)))) -> b#(a(x1)) -> b#(x1)
        SCC Processor:
         #sccs: 0
         #rules: 0
         #arcs: 1/4