NO

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> a(a(a(c(b(x1)))))
  c(c(a(x1))) -> b(x1)
  DP Processor:
   DPs:
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> c#(b(x1))
    b#(a(x1)) -> a#(c(b(x1)))
    b#(a(x1)) -> a#(a(c(b(x1))))
    b#(a(x1)) -> a#(a(a(c(b(x1)))))
    c#(c(a(x1))) -> b#(x1)
   TRS:
    a(x1) -> x1
    b(a(x1)) -> a(a(a(c(b(x1)))))
    c(c(a(x1))) -> b(x1)
   TDG Processor:
    DPs:
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> c#(b(x1))
     b#(a(x1)) -> a#(c(b(x1)))
     b#(a(x1)) -> a#(a(c(b(x1))))
     b#(a(x1)) -> a#(a(a(c(b(x1)))))
     c#(c(a(x1))) -> b#(x1)
    TRS:
     a(x1) -> x1
     b(a(x1)) -> a(a(a(c(b(x1)))))
     c(c(a(x1))) -> b(x1)
    graph:
     c#(c(a(x1))) -> b#(x1) -> b#(a(x1)) -> a#(a(a(c(b(x1)))))
     c#(c(a(x1))) -> b#(x1) -> b#(a(x1)) -> a#(a(c(b(x1))))
     c#(c(a(x1))) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1)))
     c#(c(a(x1))) -> b#(x1) -> b#(a(x1)) -> c#(b(x1))
     c#(c(a(x1))) -> b#(x1) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> c#(b(x1)) -> c#(c(a(x1))) -> b#(x1)
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(a(a(c(b(x1)))))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(a(c(b(x1))))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1)))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 11/36
     DPs:
      c#(c(a(x1))) -> b#(x1)
      b#(a(x1)) -> b#(x1)
      b#(a(x1)) -> c#(b(x1))
     TRS:
      a(x1) -> x1
      b(a(x1)) -> a(a(a(c(b(x1)))))
      c(c(a(x1))) -> b(x1)
     Loop Processor:
      loop length: 14
      terms:
       b(a(a(c(b(a(a(c(b(x1)))))))))
       a(a(a(c(b(a(c(b(a(a(c(b(x1))))))))))))
       a(a(a(c(b(a(c(a(a(a(c(b(a(c(b(x1)))))))))))))))
       a(a(a(c(b(a(c(a(a(c(b(a(c(b(x1))))))))))))))
       a(a(a(c(a(a(a(c(b(c(a(a(c(b(a(c(b(x1)))))))))))))))))
       a(a(a(c(a(a(a(c(b(c(a(a(c(a(a(a(c(b(c(b(x1))))))))))))))))))))
       a(a(a(c(a(a(a(c(b(c(a(c(a(a(a(c(b(c(b(x1)))))))))))))))))))
       a(a(a(c(a(a(a(c(b(c(c(a(a(a(c(b(c(b(x1))))))))))))))))))
       a(a(a(c(a(a(a(c(b(b(a(a(c(b(c(b(x1))))))))))))))))
       a(a(a(c(a(a(c(b(b(a(a(c(b(c(b(x1)))))))))))))))
       a(a(a(c(a(c(b(b(a(a(c(b(c(b(x1))))))))))))))
       a(a(a(c(c(b(b(a(a(c(b(c(b(x1)))))))))))))
       a(a(a(c(c(b(a(a(a(c(b(a(c(b(c(b(x1))))))))))))))))
       a(a(a(c(c(a(a(a(c(b(a(a(c(b(a(c(b(c(b(x1)))))))))))))))))))
      context: a(a(a([])))
      substitution:
       x1 -> a(c(b(c(b(x1)))))
      Qed