MAYBE

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

Proof:
 DP Processor:
  DPs:
   a#(a(a(x1))) -> b#(x1)
   b#(b(x1)) -> a#(b(x1))
   b#(b(x1)) -> b#(a(b(x1)))
   b#(b(x1)) -> a#(x1)
   b#(b(x1)) -> a#(a(x1))
  TRS:
   a(a(a(x1))) -> b(x1)
   b(b(x1)) -> b(a(b(x1)))
   b(b(x1)) -> a(a(x1))
  ADG Processor:
   DPs:
    a#(a(a(x1))) -> b#(x1)
    b#(b(x1)) -> a#(b(x1))
    b#(b(x1)) -> b#(a(b(x1)))
    b#(b(x1)) -> a#(x1)
    b#(b(x1)) -> a#(a(x1))
   TRS:
    a(a(a(x1))) -> b(x1)
    b(b(x1)) -> b(a(b(x1)))
    b(b(x1)) -> a(a(x1))
   graph:
    b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> 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#(x1)
    b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(a(x1))
    b#(b(x1)) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(x1)
    b#(b(x1)) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(x1)
    b#(b(x1)) -> a#(x1) -> a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(b(x1))
    a#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> b#(a(b(x1)))
    a#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(a(x1))
   Restore Modifier:
    DPs:
     a#(a(a(x1))) -> b#(x1)
     b#(b(x1)) -> a#(b(x1))
     b#(b(x1)) -> b#(a(b(x1)))
     b#(b(x1)) -> a#(x1)
     b#(b(x1)) -> a#(a(x1))
    TRS:
     a(a(a(x1))) -> b(x1)
     b(b(x1)) -> b(a(b(x1)))
     b(b(x1)) -> a(a(x1))
    SCC Processor:
     #sccs: 1
     #rules: 5
     #arcs: 11/25
     DPs:
      b#(b(x1)) -> b#(a(b(x1)))
      b#(b(x1)) -> a#(a(x1))
      a#(a(a(x1))) -> b#(x1)
      b#(b(x1)) -> a#(x1)
      b#(b(x1)) -> a#(b(x1))
     TRS:
      a(a(a(x1))) -> b(x1)
      b(b(x1)) -> b(a(b(x1)))
      b(b(x1)) -> a(a(x1))
     Open