YES

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

Proof:
 String Reversal Processor:
  b(a(x1)) -> b(b(b(x1)))
  a(b(x1)) -> a(a(a(x1)))
  a(x1) -> x1
  b(x1) -> x1
  DP Processor:
   DPs:
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> b#(b(x1))
    b#(a(x1)) -> b#(b(b(x1)))
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> a#(a(x1))
    a#(b(x1)) -> a#(a(a(x1)))
   TRS:
    b(a(x1)) -> b(b(b(x1)))
    a(b(x1)) -> a(a(a(x1)))
    a(x1) -> x1
    b(x1) -> x1
   TDG Processor:
    DPs:
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> b#(b(x1))
     b#(a(x1)) -> b#(b(b(x1)))
     a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> a#(a(x1))
     a#(b(x1)) -> a#(a(a(x1)))
    TRS:
     b(a(x1)) -> b(b(b(x1)))
     a(b(x1)) -> a(a(a(x1)))
     a(x1) -> x1
     b(x1) -> x1
    graph:
     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(x1))
     a#(b(x1)) -> a#(a(a(x1))) -> a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(a(a(x1)))
     a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(a(x1))
     a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(a(x1)))
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
     b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) -> b#(b(b(x1)))
     b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) -> b#(b(x1))
     b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(b(x1)))
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(b(x1)))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    CDG Processor:
     DPs:
      b#(a(x1)) -> b#(x1)
      b#(a(x1)) -> b#(b(x1))
      b#(a(x1)) -> b#(b(b(x1)))
      a#(b(x1)) -> a#(x1)
      a#(b(x1)) -> a#(a(x1))
      a#(b(x1)) -> a#(a(a(x1)))
     TRS:
      b(a(x1)) -> b(b(b(x1)))
      a(b(x1)) -> a(a(a(x1)))
      a(x1) -> x1
      b(x1) -> x1
     graph:
      
     Qed