YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> a#(a(x1))
   a#(a(b(x1))) -> b#(a(a(x1)))
   a#(a(b(x1))) -> b#(b(a(a(x1))))
   b#(a(x1)) -> b#(x1)
   b#(a(x1)) -> a#(c(b(x1)))
  TRS:
   a(a(b(x1))) -> b(b(a(a(x1))))
   b(a(x1)) -> a(c(b(x1)))
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> b#(b(a(a(x1))))
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> a#(c(b(x1)))
   TRS:
    a(a(b(x1))) -> b(b(a(a(x1))))
    b(a(x1)) -> a(c(b(x1)))
   graph:
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1)))
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> a#(c(b(x1))) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
    b#(a(x1)) -> a#(c(b(x1))) -> a#(a(b(x1))) -> b#(a(a(x1)))
    b#(a(x1)) -> a#(c(b(x1))) -> a#(a(b(x1))) -> a#(a(x1))
    b#(a(x1)) -> a#(c(b(x1))) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(x1)) -> a#(c(b(x1)))
    a#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(x1)) -> b#(x1)
    a#(a(b(x1))) -> b#(b(a(a(x1)))) -> b#(a(x1)) -> a#(c(b(x1)))
    a#(a(b(x1))) -> b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(x1)
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
   EDG Processor:
    DPs:
     a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(a(x1))
     a#(a(b(x1))) -> b#(a(a(x1)))
     a#(a(b(x1))) -> b#(b(a(a(x1))))
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> a#(c(b(x1)))
    TRS:
     a(a(b(x1))) -> b(b(a(a(x1))))
     b(a(x1)) -> a(c(b(x1)))
    graph:
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1)))
     a#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(x1)) -> b#(x1)
     a#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(x1)) -> a#(c(b(x1)))
     a#(a(b(x1))) -> b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(x1)
     a#(a(b(x1))) -> b#(b(a(a(x1)))) -> b#(a(x1)) -> a#(c(b(x1)))
     a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
     a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1)))
     a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1)))
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
    CDG Processor:
     DPs:
      a#(a(b(x1))) -> a#(x1)
      a#(a(b(x1))) -> a#(a(x1))
      a#(a(b(x1))) -> b#(a(a(x1)))
      a#(a(b(x1))) -> b#(b(a(a(x1))))
      b#(a(x1)) -> b#(x1)
      b#(a(x1)) -> a#(c(b(x1)))
     TRS:
      a(a(b(x1))) -> b(b(a(a(x1))))
      b(a(x1)) -> a(c(b(x1)))
     graph:
      a#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(x1)) -> a#(c(b(x1)))
      a#(a(b(x1))) -> b#(a(a(x1))) -> b#(a(x1)) -> b#(x1)
      a#(a(b(x1))) -> b#(b(a(a(x1)))) -> b#(a(x1)) -> a#(c(b(x1)))
      a#(a(b(x1))) -> b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(x1)
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 4/36