YES

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

Proof:
 String Reversal Processor:
  c(b(a(x1))) -> a(a(a(b(b(b(c(c(c(x1)))))))))
  b(c(x1)) -> a(a(a(x1)))
  a(x1) -> x1
  b(x1) -> x1
  c(x1) -> x1
  DP Processor:
   DPs:
    c#(b(a(x1))) -> c#(x1)
    c#(b(a(x1))) -> c#(c(x1))
    c#(b(a(x1))) -> c#(c(c(x1)))
    c#(b(a(x1))) -> b#(c(c(c(x1))))
    c#(b(a(x1))) -> b#(b(c(c(c(x1)))))
    c#(b(a(x1))) -> b#(b(b(c(c(c(x1))))))
    c#(b(a(x1))) -> a#(b(b(b(c(c(c(x1)))))))
    c#(b(a(x1))) -> a#(a(b(b(b(c(c(c(x1))))))))
    c#(b(a(x1))) -> a#(a(a(b(b(b(c(c(c(x1)))))))))
    b#(c(x1)) -> a#(x1)
    b#(c(x1)) -> a#(a(x1))
    b#(c(x1)) -> a#(a(a(x1)))
   TRS:
    c(b(a(x1))) -> a(a(a(b(b(b(c(c(c(x1)))))))))
    b(c(x1)) -> a(a(a(x1)))
    a(x1) -> x1
    b(x1) -> x1
    c(x1) -> x1
   TDG Processor:
    DPs:
     c#(b(a(x1))) -> c#(x1)
     c#(b(a(x1))) -> c#(c(x1))
     c#(b(a(x1))) -> c#(c(c(x1)))
     c#(b(a(x1))) -> b#(c(c(c(x1))))
     c#(b(a(x1))) -> b#(b(c(c(c(x1)))))
     c#(b(a(x1))) -> b#(b(b(c(c(c(x1))))))
     c#(b(a(x1))) -> a#(b(b(b(c(c(c(x1)))))))
     c#(b(a(x1))) -> a#(a(b(b(b(c(c(c(x1))))))))
     c#(b(a(x1))) -> a#(a(a(b(b(b(c(c(c(x1)))))))))
     b#(c(x1)) -> a#(x1)
     b#(c(x1)) -> a#(a(x1))
     b#(c(x1)) -> a#(a(a(x1)))
    TRS:
     c(b(a(x1))) -> a(a(a(b(b(b(c(c(c(x1)))))))))
     b(c(x1)) -> a(a(a(x1)))
     a(x1) -> x1
     b(x1) -> x1
     c(x1) -> x1
    graph:
     c#(b(a(x1))) -> b#(b(b(c(c(c(x1)))))) ->
     b#(c(x1)) -> a#(a(a(x1)))
     c#(b(a(x1))) -> b#(b(b(c(c(c(x1)))))) ->
     b#(c(x1)) -> a#(a(x1))
     c#(b(a(x1))) -> b#(b(b(c(c(c(x1)))))) -> b#(c(x1)) -> a#(x1)
     c#(b(a(x1))) -> b#(b(c(c(c(x1))))) ->
     b#(c(x1)) -> a#(a(a(x1)))
     c#(b(a(x1))) -> b#(b(c(c(c(x1))))) -> b#(c(x1)) -> a#(a(x1))
     c#(b(a(x1))) -> b#(b(c(c(c(x1))))) -> b#(c(x1)) -> a#(x1)
     c#(b(a(x1))) -> b#(c(c(c(x1)))) -> b#(c(x1)) -> a#(a(a(x1)))
     c#(b(a(x1))) -> b#(c(c(c(x1)))) -> b#(c(x1)) -> a#(a(x1))
     c#(b(a(x1))) -> b#(c(c(c(x1)))) -> b#(c(x1)) -> a#(x1)
     c#(b(a(x1))) -> c#(c(c(x1))) ->
     c#(b(a(x1))) -> a#(a(a(b(b(b(c(c(c(x1)))))))))
     c#(b(a(x1))) -> c#(c(c(x1))) ->
     c#(b(a(x1))) -> a#(a(b(b(b(c(c(c(x1))))))))
     c#(b(a(x1))) -> c#(c(c(x1))) ->
     c#(b(a(x1))) -> a#(b(b(b(c(c(c(x1)))))))
     c#(b(a(x1))) -> c#(c(c(x1))) ->
     c#(b(a(x1))) -> b#(b(b(c(c(c(x1))))))
     c#(b(a(x1))) -> c#(c(c(x1))) -> c#(b(a(x1))) -> b#(b(c(c(c(x1)))))
     c#(b(a(x1))) -> c#(c(c(x1))) -> c#(b(a(x1))) -> b#(c(c(c(x1))))
     c#(b(a(x1))) -> c#(c(c(x1))) -> c#(b(a(x1))) -> c#(c(c(x1)))
     c#(b(a(x1))) -> c#(c(c(x1))) -> c#(b(a(x1))) -> c#(c(x1))
     c#(b(a(x1))) -> c#(c(c(x1))) -> c#(b(a(x1))) -> c#(x1)
     c#(b(a(x1))) -> c#(c(x1)) ->
     c#(b(a(x1))) -> a#(a(a(b(b(b(c(c(c(x1)))))))))
     c#(b(a(x1))) -> c#(c(x1)) ->
     c#(b(a(x1))) -> a#(a(b(b(b(c(c(c(x1))))))))
     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> a#(b(b(b(c(c(c(x1)))))))
     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> b#(b(b(c(c(c(x1))))))
     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> b#(b(c(c(c(x1)))))
     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> b#(c(c(c(x1))))
     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(c(c(x1)))
     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(c(x1))
     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(x1)
     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> a#(a(a(b(b(b(c(c(c(x1)))))))))
     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> a#(a(b(b(b(c(c(c(x1))))))))
     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> a#(b(b(b(c(c(c(x1)))))))
     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> b#(b(b(c(c(c(x1))))))
     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> b#(b(c(c(c(x1)))))
     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> b#(c(c(c(x1))))
     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(c(c(x1)))
     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(c(x1))
     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 36/144
     DPs:
      c#(b(a(x1))) -> c#(c(c(x1)))
      c#(b(a(x1))) -> c#(x1)
      c#(b(a(x1))) -> c#(c(x1))
     TRS:
      c(b(a(x1))) -> a(a(a(b(b(b(c(c(c(x1)))))))))
      b(c(x1)) -> a(a(a(x1)))
      a(x1) -> x1
      b(x1) -> x1
      c(x1) -> x1
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       c(b(a(x1))) -> a(a(a(b(b(b(c(c(c(x1)))))))))
       b(c(x1)) -> a(a(a(x1)))
       a(x1) -> x1
       b(x1) -> x1
       c(x1) -> x1
      interpretation:
                 [0  1 ]  
       [b](x0) = [-& 0 ]x0,
       
       [c#](x0) = [3 3]x0,
       
                 [0 0]  
       [c](x0) = [0 0]x0,
       
                 [0 0]  
       [a](x0) = [0 0]x0
      orientation:
       c#(b(a(x1))) = [4 4]x1 >= [3 3]x1 = c#(c(c(x1)))
       
       c#(b(a(x1))) = [4 4]x1 >= [3 3]x1 = c#(x1)
       
       c#(b(a(x1))) = [4 4]x1 >= [3 3]x1 = c#(c(x1))
       
                     [1 1]      [1 1]                                  
       c(b(a(x1))) = [1 1]x1 >= [1 1]x1 = a(a(a(b(b(b(c(c(c(x1)))))))))
       
                  [1 1]      [0 0]                
       b(c(x1)) = [0 0]x1 >= [0 0]x1 = a(a(a(x1)))
       
               [0 0]             
       a(x1) = [0 0]x1 >= x1 = x1
       
               [0  1 ]             
       b(x1) = [-& 0 ]x1 >= x1 = x1
       
               [0 0]             
       c(x1) = [0 0]x1 >= x1 = x1
      problem:
       DPs:
        
       TRS:
        c(b(a(x1))) -> a(a(a(b(b(b(c(c(c(x1)))))))))
        b(c(x1)) -> a(a(a(x1)))
        a(x1) -> x1
        b(x1) -> x1
        c(x1) -> x1
      Qed