NO

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> a(c(a(a(b(b(x1))))))
  b(x1) -> x1
  c(c(x1)) -> x1
  DP Processor:
   DPs:
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> b#(b(x1))
    b#(a(x1)) -> a#(b(b(x1)))
    b#(a(x1)) -> a#(a(b(b(x1))))
    b#(a(x1)) -> c#(a(a(b(b(x1)))))
    b#(a(x1)) -> a#(c(a(a(b(b(x1))))))
   TRS:
    a(x1) -> x1
    b(a(x1)) -> a(c(a(a(b(b(x1))))))
    b(x1) -> x1
    c(c(x1)) -> x1
   TDG Processor:
    DPs:
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> b#(b(x1))
     b#(a(x1)) -> a#(b(b(x1)))
     b#(a(x1)) -> a#(a(b(b(x1))))
     b#(a(x1)) -> c#(a(a(b(b(x1)))))
     b#(a(x1)) -> a#(c(a(a(b(b(x1))))))
    TRS:
     a(x1) -> x1
     b(a(x1)) -> a(c(a(a(b(b(x1))))))
     b(x1) -> x1
     c(c(x1)) -> x1
    graph:
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(c(a(a(b(b(x1))))))
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(a(b(b(x1)))))
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(a(b(b(x1))))
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(b(x1)))
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(a(a(b(b(x1))))))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(a(b(b(x1)))))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(a(b(b(x1))))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(x1)))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 12/36
     DPs:
      b#(a(x1)) -> b#(b(x1))
      b#(a(x1)) -> b#(x1)
     TRS:
      a(x1) -> x1
      b(a(x1)) -> a(c(a(a(b(b(x1))))))
      b(x1) -> x1
      c(c(x1)) -> x1
     Loop Processor:
      loop length: 10
      terms:
       b(b(a(a(a(a(x1))))))
       b(a(c(a(a(b(b(a(a(a(x1))))))))))
       b(a(c(a(b(b(a(a(a(x1)))))))))
       b(a(c(a(b(a(a(a(x1))))))))
       b(a(c(a(a(c(a(a(b(b(a(a(x1))))))))))))
       b(a(c(a(c(a(a(b(b(a(a(x1)))))))))))
       b(a(c(a(c(a(a(b(a(a(x1))))))))))
       b(a(c(c(a(a(b(a(a(x1)))))))))
       a(c(a(a(b(b(c(c(a(a(b(a(a(x1)))))))))))))
       a(c(a(a(b(b(a(a(b(a(a(x1)))))))))))
      context: a(c(a(a([]))))
      substitution:
       x1 -> x1
      Qed