NO

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

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