NO

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

Proof:
 DP Processor:
  DPs:
   a#(b(c(x1))) -> a#(x1)
   a#(b(c(x1))) -> a#(a(x1))
   a#(b(c(x1))) -> c#(b(a(a(x1))))
   a#(b(c(x1))) -> c#(c(b(a(a(x1)))))
  TRS:
   a(x1) -> b(x1)
   a(b(c(x1))) -> c(c(b(a(a(x1)))))
   c(c(x1)) -> x1
  TDG Processor:
   DPs:
    a#(b(c(x1))) -> a#(x1)
    a#(b(c(x1))) -> a#(a(x1))
    a#(b(c(x1))) -> c#(b(a(a(x1))))
    a#(b(c(x1))) -> c#(c(b(a(a(x1)))))
   TRS:
    a(x1) -> b(x1)
    a(b(c(x1))) -> c(c(b(a(a(x1)))))
    c(c(x1)) -> x1
   graph:
    a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> c#(c(b(a(a(x1)))))
    a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> c#(b(a(a(x1))))
    a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1))
    a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> a#(x1)
    a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(c(b(a(a(x1)))))
    a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(b(a(a(x1))))
    a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(a(x1))
    a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 8/16
    DPs:
     a#(b(c(x1))) -> a#(a(x1))
     a#(b(c(x1))) -> a#(x1)
    TRS:
     a(x1) -> b(x1)
     a(b(c(x1))) -> c(c(b(a(a(x1)))))
     c(c(x1)) -> x1
    Loop Processor:
     loop length: 14
     terms:
      a(b(c(b(c(c(b(a(b(c(b(a(a(b(x1))))))))))))))
      c(c(b(a(a(b(c(c(b(a(b(c(b(a(a(b(x1))))))))))))))))
      c(c(b(a(c(c(b(a(a(c(b(a(b(c(b(a(a(b(x1))))))))))))))))))
      c(c(b(a(b(a(a(c(b(a(b(c(b(a(a(b(x1))))))))))))))))
      c(c(b(a(b(a(b(c(b(a(b(c(b(a(a(b(x1))))))))))))))))
      c(c(b(a(b(c(c(b(a(a(b(a(b(c(b(a(a(b(x1))))))))))))))))))
      c(c(b(a(b(c(c(b(a(a(b(c(c(b(a(a(b(a(a(b(x1))))))))))))))))))))
      c(c(b(a(b(c(c(b(a(c(c(b(a(a(c(b(a(a(b(a(a(b(x1))))))))))))))))))))))
      c(c(b(a(b(c(c(b(a(c(c(b(a(b(c(b(a(a(b(a(a(b(x1))))))))))))))))))))))
      c(c(b(a(b(c(c(b(a(b(a(b(c(b(a(a(b(a(a(b(x1))))))))))))))))))))
      c(c(b(c(c(b(a(a(c(b(a(b(a(b(c(b(a(a(b(a(a(b(x1))))))))))))))))))))))
      c(c(b(c(c(b(a(b(c(b(a(b(a(b(c(b(a(a(b(a(a(b(x1))))))))))))))))))))))
      c(c(b(c(c(b(a(b(c(b(a(b(c(c(b(a(a(b(a(a(b(a(a(b(x1))))))))))))))))))))))))
      c(c(b(c(c(b(a(b(c(b(c(c(b(a(a(c(b(a(a(b(a(a(b(a(a(b(x1))))))))))))))))))))))))))
     context: c(c(b(c(c(b([]))))))
     substitution:
      x1 -> a(a(b(a(a(b(x1))))))
     Qed