YES

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

Proof:
 String Reversal Processor:
  a(a(a(a(x1)))) -> b(b(b(b(b(b(a(a(x1))))))))
  a(a(b(b(x1)))) -> c(c(b(b(b(b(x1))))))
  c(c(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(a(a(a(a(x1))))))))
  DP Processor:
   DPs:
    a#(a(b(b(x1)))) -> c#(b(b(b(b(x1)))))
    a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1))))))
    c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1)))
    c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1))))
    c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1)))))
    c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1))))))
   TRS:
    a(a(a(a(x1)))) -> b(b(b(b(b(b(a(a(x1))))))))
    a(a(b(b(x1)))) -> c(c(b(b(b(b(x1))))))
    c(c(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(a(a(a(a(x1))))))))
   TDG Processor:
    DPs:
     a#(a(b(b(x1)))) -> c#(b(b(b(b(x1)))))
     a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1))))))
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1)))
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1))))
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1)))))
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1))))))
    TRS:
     a(a(a(a(x1)))) -> b(b(b(b(b(b(a(a(x1))))))))
     a(a(b(b(x1)))) -> c(c(b(b(b(b(x1))))))
     c(c(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(a(a(a(a(x1))))))))
    graph:
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) ->
     a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1))))))
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) ->
     a#(a(b(b(x1)))) -> c#(b(b(b(b(x1)))))
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) ->
     a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1))))))
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) ->
     a#(a(b(b(x1)))) -> c#(b(b(b(b(x1)))))
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) ->
     a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1))))))
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) ->
     a#(a(b(b(x1)))) -> c#(b(b(b(b(x1)))))
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) ->
     a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1))))))
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) ->
     a#(a(b(b(x1)))) -> c#(b(b(b(b(x1)))))
     a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) ->
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1))))))
     a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) ->
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1)))))
     a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) ->
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1))))
     a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) ->
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1)))
     a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) ->
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1))))))
     a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) ->
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1)))))
     a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) ->
     c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1))))
     a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) -> c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1)))
    EDG Processor:
     DPs:
      a#(a(b(b(x1)))) -> c#(b(b(b(b(x1)))))
      a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1))))))
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1)))
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1))))
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1)))))
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1))))))
     TRS:
      a(a(a(a(x1)))) -> b(b(b(b(b(b(a(a(x1))))))))
      a(a(b(b(x1)))) -> c(c(b(b(b(b(x1))))))
      c(c(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(a(a(a(a(x1))))))))
     graph:
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) ->
      a#(a(b(b(x1)))) -> c#(b(b(b(b(x1)))))
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) ->
      a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1))))))
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) ->
      a#(a(b(b(x1)))) -> c#(b(b(b(b(x1)))))
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) ->
      a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1))))))
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) ->
      a#(a(b(b(x1)))) -> c#(b(b(b(b(x1)))))
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) ->
      a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1))))))
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) ->
      a#(a(b(b(x1)))) -> c#(b(b(b(b(x1)))))
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) ->
      a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1))))))
      a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) ->
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1)))
      a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) ->
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1))))
      a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) ->
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1)))))
      a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) ->
      c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1))))))
     SCC Processor:
      #sccs: 1
      #rules: 5
      #arcs: 12/36
      DPs:
       c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1))))))
       a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1))))))
       c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1)))))
       c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1))))
       c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1)))
      TRS:
       a(a(a(a(x1)))) -> b(b(b(b(b(b(a(a(x1))))))))
       a(a(b(b(x1)))) -> c(c(b(b(b(b(x1))))))
       c(c(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(a(a(a(a(x1))))))))
      Matrix Interpretation Processor: dim=4
       
       interpretation:
        [c#](x0) = [0 1 0 0]x0,
        
        [a#](x0) = [1 0 0 0]x0,
        
                  [0 0 0 1]  
                  [0 1 0 0]  
        [c](x0) = [0 0 0 1]x0
                  [0 1 0 0]  ,
        
                  [0 0 0 0]  
                  [0 0 1 0]  
        [b](x0) = [0 0 0 1]x0
                  [0 1 0 0]  ,
        
                  [0 0 0 1]     [0]
                  [0 0 0 1]     [0]
        [a](x0) = [0 0 0 1]x0 + [1]
                  [0 0 0 1]     [0]
       orientation:
        c#(c(b(b(b(b(a(a(x1)))))))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 = a#(a(a(a(a(a(x1))))))
        
        a#(a(b(b(x1)))) = [0 0 1 0]x1 >= [0 0 1 0]x1 = c#(c(b(b(b(b(x1))))))
        
        c#(c(b(b(b(b(a(a(x1)))))))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 = a#(a(a(a(a(x1)))))
        
        c#(c(b(b(b(b(a(a(x1)))))))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 = a#(a(a(a(x1))))
        
        c#(c(b(b(b(b(a(a(x1)))))))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 = a#(a(a(x1)))
        
                         [0 0 0 1]     [0]    [0 0 0 0]     [0]                             
                         [0 0 0 1]     [0]    [0 0 0 1]     [0]                             
        a(a(a(a(x1)))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 + [1] = b(b(b(b(b(b(a(a(x1))))))))
                         [0 0 0 1]     [0]    [0 0 0 1]     [0]                             
        
                         [0 0 1 0]     [0]    [0 0 1 0]                         
                         [0 0 1 0]     [0]    [0 0 1 0]                         
        a(a(b(b(x1)))) = [0 0 1 0]x1 + [1] >= [0 0 1 0]x1 = c(c(b(b(b(b(x1))))))
                         [0 0 1 0]     [0]    [0 0 1 0]                         
        
                                     [0 0 0 1]     [1]    [0 0 0 0]     [0]                             
                                     [0 0 0 1]     [1]    [0 0 0 1]     [0]                             
        c(c(b(b(b(b(a(a(x1)))))))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 + [0] = b(b(a(a(a(a(a(a(x1))))))))
                                     [0 0 0 1]     [1]    [0 0 0 1]     [1]                             
       problem:
        DPs:
         a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1))))))
        TRS:
         a(a(a(a(x1)))) -> b(b(b(b(b(b(a(a(x1))))))))
         a(a(b(b(x1)))) -> c(c(b(b(b(b(x1))))))
         c(c(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(a(a(a(a(x1))))))))
       EDG Processor:
        DPs:
         a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1))))))
        TRS:
         a(a(a(a(x1)))) -> b(b(b(b(b(b(a(a(x1))))))))
         a(a(b(b(x1)))) -> c(c(b(b(b(b(x1))))))
         c(c(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(a(a(a(a(x1))))))))
        graph:
         
        Qed