YES

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

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