NO

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

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