YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> b#(a(x1))
   b#(a(x1)) -> b#(x1)
   b#(a(x1)) -> a#(c(b(x1)))
   b#(a(x1)) -> a#(a(c(b(x1))))
  TRS:
   a(b(x1)) -> b(a(x1))
   b(a(x1)) -> a(a(c(b(x1))))
  TDG Processor:
   DPs:
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(a(x1))
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> a#(c(b(x1)))
    b#(a(x1)) -> a#(a(c(b(x1))))
   TRS:
    a(b(x1)) -> b(a(x1))
    b(a(x1)) -> a(a(c(b(x1))))
   graph:
    b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(a(c(b(x1))))
    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#(b(x1)) -> b#(a(x1))
    b#(a(x1)) -> a#(c(b(x1))) -> a#(b(x1)) -> a#(x1)
    b#(a(x1)) -> a#(a(c(b(x1)))) -> a#(b(x1)) -> b#(a(x1))
    b#(a(x1)) -> a#(a(c(b(x1)))) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(a(x1)) -> b#(a(x1)) -> a#(a(c(b(x1))))
    a#(b(x1)) -> b#(a(x1)) -> b#(a(x1)) -> a#(c(b(x1)))
    a#(b(x1)) -> b#(a(x1)) -> b#(a(x1)) -> b#(x1)
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(x1))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
   EDG Processor:
    DPs:
     a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> b#(a(x1))
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> a#(c(b(x1)))
     b#(a(x1)) -> a#(a(c(b(x1))))
    TRS:
     a(b(x1)) -> b(a(x1))
     b(a(x1)) -> a(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)))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(a(c(b(x1))))
     a#(b(x1)) -> b#(a(x1)) -> b#(a(x1)) -> b#(x1)
     a#(b(x1)) -> b#(a(x1)) -> b#(a(x1)) -> a#(c(b(x1)))
     a#(b(x1)) -> b#(a(x1)) -> b#(a(x1)) -> a#(a(c(b(x1))))
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(x1))
    CDG Processor:
     DPs:
      a#(b(x1)) -> a#(x1)
      a#(b(x1)) -> b#(a(x1))
      b#(a(x1)) -> b#(x1)
      b#(a(x1)) -> a#(c(b(x1)))
      b#(a(x1)) -> a#(a(c(b(x1))))
     TRS:
      a(b(x1)) -> b(a(x1))
      b(a(x1)) -> a(a(c(b(x1))))
     graph:
      a#(b(x1)) -> b#(a(x1)) -> b#(a(x1)) -> a#(a(c(b(x1))))
      a#(b(x1)) -> b#(a(x1)) -> b#(a(x1)) -> a#(c(b(x1)))
      a#(b(x1)) -> b#(a(x1)) -> b#(a(x1)) -> b#(x1)
      a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(x1))
      a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 5/25
      DPs:
       a#(b(x1)) -> a#(x1)
      TRS:
       a(b(x1)) -> b(a(x1))
       b(a(x1)) -> a(a(c(b(x1))))
      KBO Processor:
       argument filtering:
        pi(b) = [0]
        pi(a) = 0
        pi(c) = 0
        pi(a#) = 0
       weight function:
        w0 = 1
        w(a#) = w(c) = w(a) = w(b) = 1
       precedence:
        a# ~ c ~ a ~ b
       problem:
        DPs:
         
        TRS:
         a(b(x1)) -> b(a(x1))
         b(a(x1)) -> a(a(c(b(x1))))
       Qed