YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(a(x1))) -> a(a(a(c(b(x1)))))
  a(c(x1)) -> b(x1)
  DP Processor:
   DPs:
    b#(a(a(x1))) -> b#(x1)
    b#(a(a(x1))) -> a#(c(b(x1)))
    b#(a(a(x1))) -> a#(a(c(b(x1))))
    b#(a(a(x1))) -> a#(a(a(c(b(x1)))))
    a#(c(x1)) -> b#(x1)
   TRS:
    a(x1) -> x1
    b(a(a(x1))) -> a(a(a(c(b(x1)))))
    a(c(x1)) -> b(x1)
   TDG Processor:
    DPs:
     b#(a(a(x1))) -> b#(x1)
     b#(a(a(x1))) -> a#(c(b(x1)))
     b#(a(a(x1))) -> a#(a(c(b(x1))))
     b#(a(a(x1))) -> a#(a(a(c(b(x1)))))
     a#(c(x1)) -> b#(x1)
    TRS:
     a(x1) -> x1
     b(a(a(x1))) -> a(a(a(c(b(x1)))))
     a(c(x1)) -> b(x1)
    graph:
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(c(b(x1)))))
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(c(b(x1))))
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(c(b(x1)))
     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
     b#(a(a(x1))) -> a#(c(b(x1))) -> a#(c(x1)) -> b#(x1)
     b#(a(a(x1))) -> a#(a(c(b(x1)))) -> a#(c(x1)) -> b#(x1)
     b#(a(a(x1))) -> a#(a(a(c(b(x1))))) -> a#(c(x1)) -> b#(x1)
     a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(c(b(x1)))))
     a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(a(c(b(x1))))
     a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(c(b(x1)))
     a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
      [b#](x0) = [2 2]x0 + [0],
      
      [a#](x0) = [2 0]x0 + [0],
      
                [0  0 ]     [2 ]
      [c](x0) = [-& -&]x0 + [-&],
      
                [0 0]     [0]
      [b](x0) = [0 0]x0 + [0],
      
                [0 2]     [0]
      [a](x0) = [0 0]x0 + [2]
     orientation:
      b#(a(a(x1))) = [4 4]x1 + [6] >= [2 2]x1 + [0] = b#(x1)
      
      b#(a(a(x1))) = [4 4]x1 + [6] >= [2 2]x1 + [4] = a#(c(b(x1)))
      
      b#(a(a(x1))) = [4 4]x1 + [6] >= [2 2]x1 + [4] = a#(a(c(b(x1))))
      
      b#(a(a(x1))) = [4 4]x1 + [6] >= [4 4]x1 + [6] = a#(a(a(c(b(x1)))))
      
      a#(c(x1)) = [2 2]x1 + [4] >= [2 2]x1 + [0] = b#(x1)
      
              [0 2]     [0]           
      a(x1) = [0 0]x1 + [2] >= x1 = x1
      
                    [2 2]     [4]    [2 2]     [4]                    
      b(a(a(x1))) = [2 2]x1 + [4] >= [2 2]x1 + [4] = a(a(a(c(b(x1)))))
      
                 [0 0]     [2]    [0 0]     [0]        
      a(c(x1)) = [0 0]x1 + [2] >= [0 0]x1 + [0] = b(x1)
     problem:
      DPs:
       b#(a(a(x1))) -> a#(a(a(c(b(x1)))))
       a#(c(x1)) -> b#(x1)
      TRS:
       a(x1) -> x1
       b(a(a(x1))) -> a(a(a(c(b(x1)))))
       a(c(x1)) -> b(x1)
     EDG Processor:
      DPs:
       b#(a(a(x1))) -> a#(a(a(c(b(x1)))))
       a#(c(x1)) -> b#(x1)
      TRS:
       a(x1) -> x1
       b(a(a(x1))) -> a(a(a(c(b(x1)))))
       a(c(x1)) -> b(x1)
      graph:
       b#(a(a(x1))) -> a#(a(a(c(b(x1))))) -> a#(c(x1)) -> b#(x1)
       a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(c(b(x1)))))
      Arctic Interpretation Processor:
       dimension: 3
       interpretation:
        [b#](x0) = [0 0 0]x0,
        
        [a#](x0) = [0 0 1]x0 + [0],
        
                  [0  0  0 ]     [0 ]
        [c](x0) = [-& -& -&]x0 + [0 ]
                  [0  0  0 ]     [-&],
        
                  [0 0 0]     [0]
        [b](x0) = [0 0 0]x0 + [0]
                  [0 0 0]     [0],
        
                  [0 1 0]     [0]
        [a](x0) = [0 0 0]x0 + [1]
                  [0 0 0]     [1]
       orientation:
        b#(a(a(x1))) = [1 1 1]x1 + [2] >= [1 1 1]x1 + [2] = a#(a(a(c(b(x1)))))
        
        a#(c(x1)) = [1 1 1]x1 + [0] >= [0 0 0]x1 = b#(x1)
        
                [0 1 0]     [0]           
        a(x1) = [0 0 0]x1 + [1] >= x1 = x1
                [0 0 0]     [1]           
        
                      [1 1 1]     [2]    [1 1 1]     [2]                    
        b(a(a(x1))) = [1 1 1]x1 + [2] >= [1 1 1]x1 + [2] = a(a(a(c(b(x1)))))
                      [1 1 1]     [2]    [1 1 1]     [2]                    
        
                   [0 0 0]     [1]    [0 0 0]     [0]        
        a(c(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = b(x1)
                   [0 0 0]     [1]    [0 0 0]     [0]        
       problem:
        DPs:
         b#(a(a(x1))) -> a#(a(a(c(b(x1)))))
        TRS:
         a(x1) -> x1
         b(a(a(x1))) -> a(a(a(c(b(x1)))))
         a(c(x1)) -> b(x1)
       EDG Processor:
        DPs:
         b#(a(a(x1))) -> a#(a(a(c(b(x1)))))
        TRS:
         a(x1) -> x1
         b(a(a(x1))) -> a(a(a(c(b(x1)))))
         a(c(x1)) -> b(x1)
        graph:
         
        Qed