YES

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

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