YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(a(x1))) -> a(a(a(c(x1))))
  a(c(x1)) -> b(b(x1))
  DP Processor:
   DPs:
    b#(a(a(x1))) -> a#(c(x1))
    b#(a(a(x1))) -> a#(a(c(x1)))
    b#(a(a(x1))) -> a#(a(a(c(x1))))
    a#(c(x1)) -> b#(x1)
    a#(c(x1)) -> b#(b(x1))
   TRS:
    a(x1) -> x1
    b(a(a(x1))) -> a(a(a(c(x1))))
    a(c(x1)) -> b(b(x1))
   TDG Processor:
    DPs:
     b#(a(a(x1))) -> a#(c(x1))
     b#(a(a(x1))) -> a#(a(c(x1)))
     b#(a(a(x1))) -> a#(a(a(c(x1))))
     a#(c(x1)) -> b#(x1)
     a#(c(x1)) -> b#(b(x1))
    TRS:
     a(x1) -> x1
     b(a(a(x1))) -> a(a(a(c(x1))))
     a(c(x1)) -> b(b(x1))
    graph:
     b#(a(a(x1))) -> a#(c(x1)) -> a#(c(x1)) -> b#(b(x1))
     b#(a(a(x1))) -> a#(c(x1)) -> a#(c(x1)) -> b#(x1)
     b#(a(a(x1))) -> a#(a(c(x1))) -> a#(c(x1)) -> b#(b(x1))
     b#(a(a(x1))) -> a#(a(c(x1))) -> a#(c(x1)) -> b#(x1)
     b#(a(a(x1))) -> a#(a(a(c(x1)))) -> a#(c(x1)) -> b#(b(x1))
     b#(a(a(x1))) -> a#(a(a(c(x1)))) -> a#(c(x1)) -> b#(x1)
     a#(c(x1)) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(a(c(x1))))
     a#(c(x1)) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(c(x1)))
     a#(c(x1)) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(c(x1))
     a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(c(x1))))
     a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(a(c(x1)))
     a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(c(x1))
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> x1
      b(a(a(x1))) -> a(a(a(c(x1))))
      a(c(x1)) -> b(b(x1))
     interpretation:
      [b#](x0) = [-& 3 ]x0 + [0],
      
      [a#](x0) = [0 3]x0 + [0],
      
                [-& -&]     [1]
      [c](x0) = [-& 0 ]x0 + [0],
      
                [-& 0 ]     [0]
      [b](x0) = [-& 0 ]x0 + [0],
      
                [0 0]     [3]
      [a](x0) = [1 0]x0 + [0]
     orientation:
      b#(a(a(x1))) = [4 4]x1 + [7] >= [-& 3 ]x1 + [3] = a#(c(x1))
      
      b#(a(a(x1))) = [4 4]x1 + [7] >= [-& 3 ]x1 + [5] = a#(a(c(x1)))
      
      b#(a(a(x1))) = [4 4]x1 + [7] >= [-& 4 ]x1 + [7] = a#(a(a(c(x1))))
      
      a#(c(x1)) = [-& 3 ]x1 + [3] >= [-& 3 ]x1 + [0] = b#(x1)
      
      a#(c(x1)) = [-& 3 ]x1 + [3] >= [-& 3 ]x1 + [3] = b#(b(x1))
      
              [0 0]     [3]           
      a(x1) = [1 0]x1 + [0] >= x1 = x1
      
                    [1 1]     [4]    [-& 1 ]     [4]                 
      b(a(a(x1))) = [1 1]x1 + [4] >= [-& 1 ]x1 + [4] = a(a(a(c(x1))))
      
                 [-& 0 ]     [3]    [-& 0 ]     [0]           
      a(c(x1)) = [-& 0 ]x1 + [2] >= [-& 0 ]x1 + [0] = b(b(x1))
     problem:
      DPs:
       b#(a(a(x1))) -> a#(a(a(c(x1))))
       a#(c(x1)) -> b#(x1)
       a#(c(x1)) -> b#(b(x1))
      TRS:
       a(x1) -> x1
       b(a(a(x1))) -> a(a(a(c(x1))))
       a(c(x1)) -> b(b(x1))
     Restore Modifier:
      DPs:
       b#(a(a(x1))) -> a#(a(a(c(x1))))
       a#(c(x1)) -> b#(x1)
       a#(c(x1)) -> b#(b(x1))
      TRS:
       a(x1) -> x1
       b(a(a(x1))) -> a(a(a(c(x1))))
       a(c(x1)) -> b(b(x1))
      EDG Processor:
       DPs:
        b#(a(a(x1))) -> a#(a(a(c(x1))))
        a#(c(x1)) -> b#(x1)
        a#(c(x1)) -> b#(b(x1))
       TRS:
        a(x1) -> x1
        b(a(a(x1))) -> a(a(a(c(x1))))
        a(c(x1)) -> b(b(x1))
       graph:
        b#(a(a(x1))) -> a#(a(a(c(x1)))) -> a#(c(x1)) -> b#(x1)
        b#(a(a(x1))) -> a#(a(a(c(x1)))) -> a#(c(x1)) -> b#(b(x1))
        a#(c(x1)) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(a(c(x1))))
        a#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(c(x1))))
       Arctic Interpretation Processor:
        dimension: 4
        usable rules:
         a(x1) -> x1
         b(a(a(x1))) -> a(a(a(c(x1))))
         a(c(x1)) -> b(b(x1))
        interpretation:
         [b#](x0) = [0 0 0 0]x0,
         
         [a#](x0) = [0 0 1 0]x0 + [0],
         
                   [0  0  0  0 ]     [0 ]
                   [-& -& -& -&]     [-&]
         [c](x0) = [0  0  0  0 ]x0 + [0 ]
                   [0  0  0  0 ]     [0 ],
         
                   [0  0  0  0 ]     [0]
                   [0  0  0  0 ]     [0]
         [b](x0) = [0  0  0  0 ]x0 + [0]
                   [0  -& -& 0 ]     [0],
         
                   [0 0 0 0]     [0]
                   [0 0 0 0]     [0]
         [a](x0) = [0 0 0 0]x0 + [0]
                   [0 1 0 0]     [0]
        orientation:
         b#(a(a(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [1] = a#(a(a(c(x1))))
         
         a#(c(x1)) = [1 1 1 1]x1 + [1] >= [0 0 0 0]x1 = b#(x1)
         
         a#(c(x1)) = [1 1 1 1]x1 + [1] >= [0 0 0 0]x1 + [0] = b#(b(x1))
         
                 [0 0 0 0]     [0]           
                 [0 0 0 0]     [0]           
         a(x1) = [0 0 0 0]x1 + [0] >= x1 = x1
                 [0 1 0 0]     [0]           
         
                       [1 1 1 1]     [1]    [1 1 1 1]     [1]                 
                       [1 1 1 1]     [1]    [1 1 1 1]     [1]                 
         b(a(a(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [1] = a(a(a(c(x1))))
                       [1 1 1 1]     [1]    [1 1 1 1]     [1]                 
         
                    [0 0 0 0]     [0]    [0 0 0 0]     [0]           
                    [0 0 0 0]     [0]    [0 0 0 0]     [0]           
         a(c(x1)) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = b(b(x1))
                    [0 0 0 0]     [0]    [0 0 0 0]     [0]           
        problem:
         DPs:
          b#(a(a(x1))) -> a#(a(a(c(x1))))
         TRS:
          a(x1) -> x1
          b(a(a(x1))) -> a(a(a(c(x1))))
          a(c(x1)) -> b(b(x1))
        Restore Modifier:
         DPs:
          b#(a(a(x1))) -> a#(a(a(c(x1))))
         TRS:
          a(x1) -> x1
          b(a(a(x1))) -> a(a(a(c(x1))))
          a(c(x1)) -> b(b(x1))
         EDG Processor:
          DPs:
           b#(a(a(x1))) -> a#(a(a(c(x1))))
          TRS:
           a(x1) -> x1
           b(a(a(x1))) -> a(a(a(c(x1))))
           a(c(x1)) -> b(b(x1))
          graph:
           
          Qed