NO

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> c#(a(x1))
   c#(c(x1)) -> a#(b(x1))
  TRS:
   a(a(x1)) -> b(x1)
   a(b(x1)) -> c(a(x1))
   c(c(x1)) -> b(a(b(x1)))
  TDG Processor:
   DPs:
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> c#(a(x1))
    c#(c(x1)) -> a#(b(x1))
   TRS:
    a(a(x1)) -> b(x1)
    a(b(x1)) -> c(a(x1))
    c(c(x1)) -> b(a(b(x1)))
   graph:
    c#(c(x1)) -> a#(b(x1)) -> a#(b(x1)) -> c#(a(x1))
    c#(c(x1)) -> a#(b(x1)) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(b(x1))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(a(x1))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
   Loop Processor:
    loop length: 18
    terms:
     c(a(b(b(c(c(a(a(b(c(a(c(a(c(x1))))))))))))))
     c(a(b(b(c(c(b(b(c(a(c(a(c(x1)))))))))))))
     c(a(b(b(b(a(b(b(b(c(a(c(a(c(x1))))))))))))))
     c(c(a(b(b(a(b(b(b(c(a(c(a(c(x1))))))))))))))
     c(c(c(a(b(a(b(b(b(c(a(c(a(c(x1))))))))))))))
     b(a(b(c(a(b(a(b(b(b(c(a(c(a(c(x1)))))))))))))))
     b(a(b(c(c(a(a(b(b(b(c(a(c(a(c(x1)))))))))))))))
     b(c(a(c(c(a(a(b(b(b(c(a(c(a(c(x1)))))))))))))))
     b(c(a(c(c(b(b(b(b(c(a(c(a(c(x1))))))))))))))
     b(c(a(b(a(b(b(b(b(b(c(a(c(a(c(x1)))))))))))))))
     b(c(a(b(c(a(b(b(b(b(c(a(c(a(c(x1)))))))))))))))
     b(c(a(b(c(c(a(b(b(b(c(a(c(a(c(x1)))))))))))))))
     b(c(a(b(b(a(b(a(b(b(b(c(a(c(a(c(x1))))))))))))))))
     b(c(a(b(b(a(b(c(a(b(b(c(a(c(a(c(x1))))))))))))))))
     b(c(a(b(b(a(b(c(c(a(b(c(a(c(a(c(x1))))))))))))))))
     b(c(a(b(b(a(b(c(c(c(a(c(a(c(a(c(x1))))))))))))))))
     b(c(a(b(b(a(b(b(a(b(c(a(c(a(c(a(c(x1)))))))))))))))))
     b(c(a(b(b(c(a(b(a(b(c(a(c(a(c(a(c(x1)))))))))))))))))
    context: b([])
    substitution:
     x1 -> a(c(x1))
    Qed