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))))
     KBO Processor:
      argument filtering:
       pi(b) = [0]
       pi(a) = 0
       pi(a#) = 0
      weight function:
       w0 = 1
       w(a#) = w(a) = w(b) = 1
      precedence:
       a# ~ a ~ b
      problem:
       DPs:
        
       TRS:
        a(a(a(b(x1)))) -> b(a(a(a(x1))))
        b(b(x1)) -> a(b(a(b(x1))))
      Qed