NO

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(c(x1))
   a#(c(x1)) -> a#(x1)
   a#(c(x1)) -> a#(a(x1))
  TRS:
   a(a(b(x1))) -> b(b(c(a(c(x1)))))
   a(c(x1)) -> a(a(x1))
  EDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(c(x1))
    a#(c(x1)) -> a#(x1)
    a#(c(x1)) -> a#(a(x1))
   TRS:
    a(a(b(x1))) -> b(b(c(a(c(x1)))))
    a(c(x1)) -> a(a(x1))
   graph:
    a#(c(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(c(x1))
    a#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(c(x1))
    a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1)
    a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(a(x1))
    a#(a(b(x1))) -> a#(c(x1)) -> a#(c(x1)) -> a#(x1)
    a#(a(b(x1))) -> a#(c(x1)) -> a#(c(x1)) -> a#(a(x1))
   Loop Processor:
    loop length: 19
    terms:
     a(c(b(c(a(c(c(a(c(b(c(a(c(c(x1))))))))))))))
     a(c(b(c(a(c(c(a(a(b(c(a(c(c(x1))))))))))))))
     a(a(b(c(a(c(c(a(a(b(c(a(c(c(x1))))))))))))))
     b(b(c(a(c(c(a(c(c(a(a(b(c(a(c(c(x1))))))))))))))))
     b(b(c(a(c(c(a(c(c(a(a(b(c(a(a(c(x1))))))))))))))))
     b(b(c(a(a(c(a(c(c(a(a(b(c(a(a(c(x1))))))))))))))))
     b(b(c(a(a(c(a(c(c(b(b(c(a(c(c(a(a(c(x1))))))))))))))))))
     b(b(c(a(a(a(a(c(c(b(b(c(a(c(c(a(a(c(x1))))))))))))))))))
     b(b(c(a(a(a(a(a(c(b(b(c(a(c(c(a(a(c(x1))))))))))))))))))
     b(b(c(a(a(a(a(a(a(b(b(c(a(c(c(a(a(c(x1))))))))))))))))))
     b(b(c(a(a(a(a(b(b(c(a(c(b(c(a(c(c(a(a(c(x1))))))))))))))))))))
     b(b(c(a(a(b(b(c(a(c(b(c(a(c(b(c(a(c(c(a(a(c(x1))))))))))))))))))))))
     b(b(c(b(b(c(a(c(b(c(a(c(b(c(a(c(b(c(a(c(c(a(a(c(x1))))))))))))))))))))))))
     b(b(c(b(b(c(a(c(b(c(a(a(b(c(a(c(b(c(a(c(c(a(a(c(x1))))))))))))))))))))))))
     b(b(c(b(b(c(a(a(b(c(a(a(b(c(a(c(b(c(a(c(c(a(a(c(x1))))))))))))))))))))))))
     b(b(c(b(b(c(b(b(c(a(c(c(a(a(b(c(a(c(b(c(a(c(c(a(a(c(x1))))))))))))))))))))))))))
     b(b(c(b(b(c(b(b(c(a(c(c(b(b(c(a(c(c(a(c(b(c(a(c(c(a(a(c(x1))))))))))))))))))))))))))))
     b(b(c(b(b(c(b(b(c(a(a(c(b(b(c(a(c(c(a(c(b(c(a(c(c(a(a(c(x1))))))))))))))))))))))))))))
     b(b(c(b(b(c(b(b(c(a(a(a(b(b(c(a(c(c(a(c(b(c(a(c(c(a(a(c(x1))))))))))))))))))))))))))))
    context: b(b(c(b(b(c(b(b(c(a(b(b(c([])))))))))))))
    substitution:
     x1 -> a(a(c(x1)))
    Qed