NO

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> b#(a(x1))
   a#(b(x1)) -> c#(b(a(x1)))
   a#(b(x1)) -> b#(c(b(a(x1))))
   b#(x1) -> a#(x1)
  TRS:
   a(x1) -> x1
   a(b(x1)) -> b(c(b(a(x1))))
   b(x1) -> a(x1)
   c(c(x1)) -> x1
  TDG Processor:
   DPs:
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(a(x1))
    a#(b(x1)) -> c#(b(a(x1)))
    a#(b(x1)) -> b#(c(b(a(x1))))
    b#(x1) -> a#(x1)
   TRS:
    a(x1) -> x1
    a(b(x1)) -> b(c(b(a(x1))))
    b(x1) -> a(x1)
    c(c(x1)) -> x1
   graph:
    b#(x1) -> a#(x1) -> a#(b(x1)) -> b#(c(b(a(x1))))
    b#(x1) -> a#(x1) -> a#(b(x1)) -> c#(b(a(x1)))
    b#(x1) -> a#(x1) -> a#(b(x1)) -> b#(a(x1))
    b#(x1) -> a#(x1) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(c(b(a(x1)))) -> b#(x1) -> a#(x1)
    a#(b(x1)) -> b#(a(x1)) -> b#(x1) -> a#(x1)
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(c(b(a(x1))))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(b(a(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: 4
    #arcs: 10/25
    DPs:
     b#(x1) -> a#(x1)
     a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> b#(a(x1))
     a#(b(x1)) -> b#(c(b(a(x1))))
    TRS:
     a(x1) -> x1
     a(b(x1)) -> b(c(b(a(x1))))
     b(x1) -> a(x1)
     c(c(x1)) -> x1
    Loop Processor:
     loop length: 14
     terms:
      a(c(a(c(b(a(c(a(c(b(b(x1)))))))))))
      a(c(c(b(a(c(a(c(b(b(x1))))))))))
      a(b(a(c(a(c(b(b(x1))))))))
      a(b(a(c(c(b(b(x1)))))))
      a(b(a(b(b(x1)))))
      a(b(b(c(b(a(b(x1)))))))
      a(b(b(c(b(b(x1))))))
      b(c(b(a(b(c(b(b(x1))))))))
      b(c(b(b(c(b(a(c(b(b(x1))))))))))
      b(c(b(b(c(b(c(b(b(x1)))))))))
      b(c(a(b(c(b(c(b(b(x1)))))))))
      b(c(b(c(b(a(c(b(c(b(b(x1)))))))))))
      b(c(a(c(b(a(c(b(c(b(b(x1)))))))))))
      b(c(a(c(b(a(c(a(c(b(b(x1)))))))))))
     context: []
     substitution:
      x1 -> x1
     Qed