NO

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> a#(a(x1))
   a#(b(x1)) -> c#(a(a(x1)))
   a#(b(x1)) -> a#(c(a(a(x1))))
   a#(b(x1)) -> c#(b(a(c(a(a(x1))))))
  TRS:
   a(x1) -> x1
   a(b(x1)) -> b(c(b(a(c(a(a(x1)))))))
   c(c(x1)) -> x1
  TDG Processor:
   DPs:
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> a#(a(x1))
    a#(b(x1)) -> c#(a(a(x1)))
    a#(b(x1)) -> a#(c(a(a(x1))))
    a#(b(x1)) -> c#(b(a(c(a(a(x1))))))
   TRS:
    a(x1) -> x1
    a(b(x1)) -> b(c(b(a(c(a(a(x1)))))))
    c(c(x1)) -> x1
   graph:
    a#(b(x1)) -> a#(c(a(a(x1)))) -> a#(b(x1)) -> c#(b(a(c(a(a(x1))))))
    a#(b(x1)) -> a#(c(a(a(x1)))) -> a#(b(x1)) -> a#(c(a(a(x1))))
    a#(b(x1)) -> a#(c(a(a(x1)))) -> a#(b(x1)) -> c#(a(a(x1)))
    a#(b(x1)) -> a#(c(a(a(x1)))) -> a#(b(x1)) -> a#(a(x1))
    a#(b(x1)) -> a#(c(a(a(x1)))) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> c#(b(a(c(a(a(x1))))))
    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(c(a(a(x1))))
    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> c#(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)) -> c#(b(a(c(a(a(x1))))))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(c(a(a(x1))))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(a(a(x1)))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 15/25
    DPs:
     a#(b(x1)) -> a#(c(a(a(x1))))
     a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> a#(a(x1))
    TRS:
     a(x1) -> x1
     a(b(x1)) -> b(c(b(a(c(a(a(x1)))))))
     c(c(x1)) -> x1
    Loop Processor:
     loop length: 13
     terms:
      a(c(c(b(a(b(a(c(x1))))))))
      a(c(c(b(a(b(c(x1)))))))
      a(b(a(b(c(x1)))))
      b(c(b(a(c(a(a(a(b(c(x1))))))))))
      b(c(b(a(c(a(a(b(c(b(a(c(a(a(c(x1)))))))))))))))
      b(c(b(a(c(a(a(b(c(b(a(c(a(c(x1))))))))))))))
      b(c(b(a(c(a(a(b(c(b(a(c(c(x1)))))))))))))
      b(c(b(a(c(a(b(c(b(a(c(a(a(c(b(a(c(c(x1))))))))))))))))))
      b(c(b(a(c(a(b(c(b(a(c(a(c(b(a(c(c(x1)))))))))))))))))
      b(c(b(a(c(b(c(b(a(c(a(a(c(b(a(c(a(c(b(a(c(c(x1))))))))))))))))))))))
      b(c(b(a(c(b(c(b(a(c(a(a(c(b(a(c(c(b(a(c(c(x1)))))))))))))))))))))
      b(c(b(a(c(b(c(b(a(c(a(a(c(b(a(b(a(c(c(x1)))))))))))))))))))
      b(c(b(a(c(b(c(b(a(c(a(c(b(a(b(a(c(c(x1))))))))))))))))))
     context: b(c(b(a(c(b(c(b([]))))))))
     substitution:
      x1 -> c(x1)
     Qed