YES

Problem:
 a(a(a(b(x1)))) -> b(a(a(a(x1))))
 b(b(x1)) -> a(b(a(b(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#(b(x1)) -> a#(b(x1))
   b#(b(x1)) -> b#(a(b(x1)))
   b#(b(x1)) -> a#(b(a(b(x1))))
  TRS:
   a(a(a(b(x1)))) -> b(a(a(a(x1))))
   b(b(x1)) -> a(b(a(b(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#(b(x1)) -> a#(b(x1))
    b#(b(x1)) -> b#(a(b(x1)))
    b#(b(x1)) -> a#(b(a(b(x1))))
   TRS:
    a(a(a(b(x1)))) -> b(a(a(a(x1))))
    b(b(x1)) -> a(b(a(b(x1))))
   graph:
    b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(b(a(b(x1))))
    b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> b#(a(b(x1)))
    b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(b(x1))
    b#(b(x1)) -> a#(b(a(b(x1)))) -> a#(a(a(b(x1)))) -> b#(a(a(a(x1))))
    b#(b(x1)) -> a#(b(a(b(x1)))) -> a#(a(a(b(x1)))) -> a#(a(a(x1)))
    b#(b(x1)) -> a#(b(a(b(x1)))) -> a#(a(a(b(x1)))) -> a#(a(x1))
    b#(b(x1)) -> a#(b(a(b(x1)))) -> a#(a(a(b(x1)))) -> a#(x1)
    b#(b(x1)) -> a#(b(x1)) -> a#(a(a(b(x1)))) -> b#(a(a(a(x1))))
    b#(b(x1)) -> a#(b(x1)) -> a#(a(a(b(x1)))) -> a#(a(a(x1)))
    b#(b(x1)) -> a#(b(x1)) -> a#(a(a(b(x1)))) -> a#(a(x1))
    b#(b(x1)) -> a#(b(x1)) -> a#(a(a(b(x1)))) -> a#(x1)
    a#(a(a(b(x1)))) -> b#(a(a(a(x1)))) ->
    b#(b(x1)) -> a#(b(a(b(x1))))
    a#(a(a(b(x1)))) -> b#(a(a(a(x1)))) ->
    b#(b(x1)) -> b#(a(b(x1)))
    a#(a(a(b(x1)))) -> b#(a(a(a(x1)))) -> b#(b(x1)) -> a#(b(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)
   CDG 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#(b(x1)) -> a#(b(x1))
     b#(b(x1)) -> b#(a(b(x1)))
     b#(b(x1)) -> a#(b(a(b(x1))))
    TRS:
     a(a(a(b(x1)))) -> b(a(a(a(x1))))
     b(b(x1)) -> a(b(a(b(x1))))
    graph:
     a#(a(a(b(x1)))) -> b#(a(a(a(x1)))) -> b#(b(x1)) -> a#(b(x1))
     a#(a(a(b(x1)))) -> b#(a(a(a(x1)))) ->
     b#(b(x1)) -> b#(a(b(x1)))
     a#(a(a(b(x1)))) -> b#(a(a(a(x1)))) ->
     b#(b(x1)) -> a#(b(a(b(x1))))
     a#(a(a(b(x1)))) -> 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#(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)))) -> b#(a(a(a(x1))))
     a#(a(a(b(x1)))) -> a#(a(x1)) -> a#(a(a(b(x1)))) -> 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#(a(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#(x1) -> a#(a(a(b(x1)))) -> 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#(a(a(x1)))
     a#(a(a(b(x1)))) -> a#(x1) -> a#(a(a(b(x1)))) -> b#(a(a(a(x1))))
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 15/49
     DPs:
      a#(a(a(b(x1)))) -> a#(a(a(x1)))
      a#(a(a(b(x1)))) -> a#(a(x1))
      a#(a(a(b(x1)))) -> a#(x1)
     TRS:
      a(a(a(b(x1)))) -> b(a(a(a(x1))))
      b(b(x1)) -> a(b(a(b(x1))))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [a#](x0) = x0 + -7,
       
       [a](x0) = x0,
       
       [b](x0) = 4x0 + -1
      orientation:
       a#(a(a(b(x1)))) = 4x1 + -1 >= x1 + -7 = a#(a(a(x1)))
       
       a#(a(a(b(x1)))) = 4x1 + -1 >= x1 + -7 = a#(a(x1))
       
       a#(a(a(b(x1)))) = 4x1 + -1 >= x1 + -7 = a#(x1)
       
       a(a(a(b(x1)))) = 4x1 + -1 >= 4x1 + -1 = b(a(a(a(x1))))
       
       b(b(x1)) = 8x1 + 3 >= 8x1 + 3 = a(b(a(b(x1))))
      problem:
       DPs:
        
       TRS:
        a(a(a(b(x1)))) -> b(a(a(a(x1))))
        b(b(x1)) -> a(b(a(b(x1))))
      Qed