YES

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

Proof:
 Arctic Interpretation Processor:
  dimension: 2
  interpretation:
             [0  3 ]  
   [a](x0) = [-& 0 ]x0,
   
             [2 3]  
   [b](x0) = [0 0]x0,
   
             [0 3]  
   [c](x0) = [0 0]x0
  orientation:
              [3 3]      [3 3]             
   c(c(x1)) = [0 3]x1 >= [0 0]x1 = a(b(x1))
   
           [2 3]      [0  3 ]             
   b(x1) = [0 0]x1 >= [-& 0 ]x1 = a(a(x1))
   
                 [6 7]      [5 6]                
   b(b(b(x1))) = [4 5]x1 >= [2 3]x1 = a(c(b(x1)))
   
                 [3 6]      [3 6]                
   a(c(a(x1))) = [0 3]x1 >= [0 3]x1 = a(c(c(x1)))
  problem:
   c(c(x1)) -> a(b(x1))
   b(x1) -> a(a(x1))
   a(c(a(x1))) -> a(c(c(x1)))
  String Reversal Processor:
   c(c(x1)) -> b(a(x1))
   b(x1) -> a(a(x1))
   a(c(a(x1))) -> c(c(a(x1)))
   DP Processor:
    DPs:
     c#(c(x1)) -> a#(x1)
     c#(c(x1)) -> b#(a(x1))
     b#(x1) -> a#(x1)
     b#(x1) -> a#(a(x1))
     a#(c(a(x1))) -> c#(c(a(x1)))
    TRS:
     c(c(x1)) -> b(a(x1))
     b(x1) -> a(a(x1))
     a(c(a(x1))) -> c(c(a(x1)))
    TDG Processor:
     DPs:
      c#(c(x1)) -> a#(x1)
      c#(c(x1)) -> b#(a(x1))
      b#(x1) -> a#(x1)
      b#(x1) -> a#(a(x1))
      a#(c(a(x1))) -> c#(c(a(x1)))
     TRS:
      c(c(x1)) -> b(a(x1))
      b(x1) -> a(a(x1))
      a(c(a(x1))) -> c(c(a(x1)))
     graph:
      b#(x1) -> a#(a(x1)) -> a#(c(a(x1))) -> c#(c(a(x1)))
      b#(x1) -> a#(x1) -> a#(c(a(x1))) -> c#(c(a(x1)))
      a#(c(a(x1))) -> c#(c(a(x1))) -> c#(c(x1)) -> b#(a(x1))
      a#(c(a(x1))) -> c#(c(a(x1))) -> c#(c(x1)) -> a#(x1)
      c#(c(x1)) -> b#(a(x1)) -> b#(x1) -> a#(a(x1))
      c#(c(x1)) -> b#(a(x1)) -> b#(x1) -> a#(x1)
      c#(c(x1)) -> a#(x1) -> a#(c(a(x1))) -> c#(c(a(x1)))
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [b#](x0) = [1  -&]x0 + [0],
       
       [a#](x0) = [1  -&]x0 + [0],
       
       [c#](x0) = [-& 0 ]x0 + [0],
       
                 [0  -&]     [-4]
       [a](x0) = [1  -4]x0 + [1 ],
       
                 [0 1]     [0]
       [b](x0) = [1 0]x0 + [1],
       
                 [0  3 ]     [-&]
       [c](x0) = [1  -&]x0 + [1 ]
      orientation:
       c#(c(x1)) = [1  -&]x1 + [1] >= [1  -&]x1 + [0] = a#(x1)
       
       c#(c(x1)) = [1  -&]x1 + [1] >= [1  -&]x1 + [0] = b#(a(x1))
       
       b#(x1) = [1  -&]x1 + [0] >= [1  -&]x1 + [0] = a#(x1)
       
       b#(x1) = [1  -&]x1 + [0] >= [1  -&]x1 + [0] = a#(a(x1))
       
       a#(c(a(x1))) = [5 0]x1 + [5] >= [1  -&]x1 + [1] = c#(c(a(x1)))
       
                  [4 3]     [4]    [2  -3]     [2]           
       c(c(x1)) = [1 4]x1 + [1] >= [1  -4]x1 + [1] = b(a(x1))
       
               [0 1]     [0]    [0  -&]     [-4]           
       b(x1) = [1 0]x1 + [1] >= [1  -8]x1 + [1 ] = a(a(x1))
       
                     [4  -1]     [4]    [4  -1]     [4]              
       a(c(a(x1))) = [5  0 ]x1 + [5] >= [5  0 ]x1 + [5] = c(c(a(x1)))
      problem:
       DPs:
        c#(c(x1)) -> a#(x1)
        c#(c(x1)) -> b#(a(x1))
        b#(x1) -> a#(x1)
        b#(x1) -> a#(a(x1))
       TRS:
        c(c(x1)) -> b(a(x1))
        b(x1) -> a(a(x1))
        a(c(a(x1))) -> c(c(a(x1)))
      EDG Processor:
       DPs:
        c#(c(x1)) -> a#(x1)
        c#(c(x1)) -> b#(a(x1))
        b#(x1) -> a#(x1)
        b#(x1) -> a#(a(x1))
       TRS:
        c(c(x1)) -> b(a(x1))
        b(x1) -> a(a(x1))
        a(c(a(x1))) -> c(c(a(x1)))
       graph:
        c#(c(x1)) -> b#(a(x1)) -> b#(x1) -> a#(x1)
        c#(c(x1)) -> b#(a(x1)) -> b#(x1) -> a#(a(x1))
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 2/16