YES

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

Proof:
 String Reversal Processor:
  a(x1) -> b(x1)
  b(a(x1)) -> c(a(b(x1)))
  b(b(x1)) -> x1
  c(c(x1)) -> a(x1)
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> a#(b(x1))
    b#(a(x1)) -> c#(a(b(x1)))
    c#(c(x1)) -> a#(x1)
   TRS:
    a(x1) -> b(x1)
    b(a(x1)) -> c(a(b(x1)))
    b(b(x1)) -> x1
    c(c(x1)) -> a(x1)
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> a#(b(x1))
     b#(a(x1)) -> c#(a(b(x1)))
     c#(c(x1)) -> a#(x1)
    TRS:
     a(x1) -> b(x1)
     b(a(x1)) -> c(a(b(x1)))
     b(b(x1)) -> x1
     c(c(x1)) -> a(x1)
    graph:
     c#(c(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
     b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> a#(x1)
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1)))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> a#(b(x1)) -> a#(x1) -> b#(x1)
     a#(x1) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1)))
     a#(x1) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
     a#(x1) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    Arctic Interpretation Processor:
     dimension: 3
     interpretation:
      [c#](x0) = [1 0 1]x0 + [0],
      
      [b#](x0) = [1 0 0]x0,
      
      [a#](x0) = [1 0 0]x0 + [0],
      
                [0 1 0]     [0 ]
      [c](x0) = [0 0 0]x0 + [-&]
                [0 0 0]     [0 ],
      
                [0  0  -&]     [-&]
      [b](x0) = [0  0  -&]x0 + [-&]
                [0  1  0 ]     [0 ],
      
                [1  1  0 ]     [0 ]
      [a](x0) = [0  0  -&]x0 + [-&]
                [0  1  0 ]     [0 ]
     orientation:
      a#(x1) = [1 0 0]x1 + [0] >= [1 0 0]x1 = b#(x1)
      
      b#(a(x1)) = [2 2 1]x1 + [1] >= [1 0 0]x1 = b#(x1)
      
      b#(a(x1)) = [2 2 1]x1 + [1] >= [1 1 0]x1 + [0] = a#(b(x1))
      
      b#(a(x1)) = [2 2 1]x1 + [1] >= [2 2 1]x1 + [1] = c#(a(b(x1)))
      
      c#(c(x1)) = [1 2 1]x1 + [1] >= [1 0 0]x1 + [0] = a#(x1)
      
              [1  1  0 ]     [0 ]    [0  0  -&]     [-&]        
      a(x1) = [0  0  -&]x1 + [-&] >= [0  0  -&]x1 + [-&] = b(x1)
              [0  1  0 ]     [0 ]    [0  1  0 ]     [0 ]        
      
                 [1 1 0]     [0]    [1 1 0]     [0]              
      b(a(x1)) = [1 1 0]x1 + [0] >= [1 1 0]x1 + [0] = c(a(b(x1)))
                 [1 1 0]     [0]    [1 1 0]     [0]              
      
                 [0  0  -&]     [-&]           
      b(b(x1)) = [0  0  -&]x1 + [-&] >= x1 = x1
                 [1  1  0 ]     [0 ]           
      
                 [1 1 1]     [0]    [1  1  0 ]     [0 ]        
      c(c(x1)) = [0 1 0]x1 + [0] >= [0  0  -&]x1 + [-&] = a(x1)
                 [0 1 0]     [0]    [0  1  0 ]     [0 ]        
     problem:
      DPs:
       a#(x1) -> b#(x1)
       b#(a(x1)) -> c#(a(b(x1)))
       c#(c(x1)) -> a#(x1)
      TRS:
       a(x1) -> b(x1)
       b(a(x1)) -> c(a(b(x1)))
       b(b(x1)) -> x1
       c(c(x1)) -> a(x1)
     EDG Processor:
      DPs:
       a#(x1) -> b#(x1)
       b#(a(x1)) -> c#(a(b(x1)))
       c#(c(x1)) -> a#(x1)
      TRS:
       a(x1) -> b(x1)
       b(a(x1)) -> c(a(b(x1)))
       b(b(x1)) -> x1
       c(c(x1)) -> a(x1)
      graph:
       c#(c(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
       b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> a#(x1)
       a#(x1) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1)))
      Arctic Interpretation Processor:
       dimension: 2
       interpretation:
        [c#](x0) = [2 0]x0 + [0],
        
        [b#](x0) = [-& 3 ]x0 + [0],
        
        [a#](x0) = [-& 3 ]x0 + [0],
        
                  [-& 2 ]     [0]
        [c](x0) = [0  0 ]x0 + [2],
        
                  [0  2 ]     [0 ]
        [b](x0) = [-& 0 ]x0 + [-&],
        
                  [0 2]     [0]
        [a](x0) = [0 2]x0 + [2]
       orientation:
        a#(x1) = [-& 3 ]x1 + [0] >= [-& 3 ]x1 + [0] = b#(x1)
        
        b#(a(x1)) = [3 5]x1 + [5] >= [2 4]x1 + [2] = c#(a(b(x1)))
        
        c#(c(x1)) = [0 4]x1 + [2] >= [-& 3 ]x1 + [0] = a#(x1)
        
                [0 2]     [0]    [0  2 ]     [0 ]        
        a(x1) = [0 2]x1 + [2] >= [-& 0 ]x1 + [-&] = b(x1)
        
                   [2 4]     [4]    [2 4]     [4]              
        b(a(x1)) = [0 2]x1 + [2] >= [0 2]x1 + [2] = c(a(b(x1)))
        
                   [0  2 ]     [0 ]           
        b(b(x1)) = [-& 0 ]x1 + [-&] >= x1 = x1
        
                   [2 2]     [4]    [0 2]     [0]        
        c(c(x1)) = [0 2]x1 + [2] >= [0 2]x1 + [2] = a(x1)
       problem:
        DPs:
         a#(x1) -> b#(x1)
        TRS:
         a(x1) -> b(x1)
         b(a(x1)) -> c(a(b(x1)))
         b(b(x1)) -> x1
         c(c(x1)) -> a(x1)
       EDG Processor:
        DPs:
         a#(x1) -> b#(x1)
        TRS:
         a(x1) -> b(x1)
         b(a(x1)) -> c(a(b(x1)))
         b(b(x1)) -> x1
         c(c(x1)) -> a(x1)
        graph:
         
        Qed