YES

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

Proof:
 String Reversal Processor:
  a(a(x1)) -> b(c(a(b(x1))))
  b(b(x1)) -> a(a(x1))
  a(c(x1)) -> x1
  DP Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> a#(b(x1))
    a#(a(x1)) -> b#(c(a(b(x1))))
    b#(b(x1)) -> a#(x1)
    b#(b(x1)) -> a#(a(x1))
   TRS:
    a(a(x1)) -> b(c(a(b(x1))))
    b(b(x1)) -> a(a(x1))
    a(c(x1)) -> x1
   TDG Processor:
    DPs:
     a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> a#(b(x1))
     a#(a(x1)) -> b#(c(a(b(x1))))
     b#(b(x1)) -> a#(x1)
     b#(b(x1)) -> a#(a(x1))
    TRS:
     a(a(x1)) -> b(c(a(b(x1))))
     b(b(x1)) -> a(a(x1))
     a(c(x1)) -> x1
    graph:
     b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(c(a(b(x1))))
     b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(x1))
     b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(x1)
     b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(c(a(b(x1))))
     b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1))
     b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> b#(c(a(b(x1)))) -> b#(b(x1)) -> a#(a(x1))
     a#(a(x1)) -> b#(c(a(b(x1)))) -> b#(b(x1)) -> a#(x1)
     a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(a(x1))
     a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(x1)
     a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(c(a(b(x1))))
     a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1))
     a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1)
    EDG Processor:
     DPs:
      a#(a(x1)) -> b#(x1)
      a#(a(x1)) -> a#(b(x1))
      a#(a(x1)) -> b#(c(a(b(x1))))
      b#(b(x1)) -> a#(x1)
      b#(b(x1)) -> a#(a(x1))
     TRS:
      a(a(x1)) -> b(c(a(b(x1))))
      b(b(x1)) -> a(a(x1))
      a(c(x1)) -> x1
     graph:
      b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(x1)
      b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(x1))
      b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(c(a(b(x1))))
      b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
      b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1))
      b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(c(a(b(x1))))
      a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(x1)
      a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(a(x1))
      a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1)
      a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1))
      a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(c(a(b(x1))))
     SCC Processor:
      #sccs: 1
      #rules: 4
      #arcs: 11/25
      DPs:
       b#(b(x1)) -> a#(a(x1))
       a#(a(x1)) -> a#(b(x1))
       a#(a(x1)) -> b#(x1)
       b#(b(x1)) -> a#(x1)
      TRS:
       a(a(x1)) -> b(c(a(b(x1))))
       b(b(x1)) -> a(a(x1))
       a(c(x1)) -> x1
      Arctic Interpretation Processor:
       dimension: 1
       usable rules:
        a(a(x1)) -> b(c(a(b(x1))))
        b(b(x1)) -> a(a(x1))
        a(c(x1)) -> x1
       interpretation:
        [b#](x0) = x0 + -16,
        
        [b](x0) = 4x0 + 4,
        
        [a#](x0) = -2x0 + 0,
        
        [a](x0) = 4x0 + 4,
        
        [c](x0) = -4x0 + 0
       orientation:
        b#(b(x1)) = 4x1 + 4 >= 2x1 + 2 = a#(a(x1))
        
        a#(a(x1)) = 2x1 + 2 >= 2x1 + 2 = a#(b(x1))
        
        a#(a(x1)) = 2x1 + 2 >= x1 + -16 = b#(x1)
        
        b#(b(x1)) = 4x1 + 4 >= -2x1 + 0 = a#(x1)
        
        a(a(x1)) = 8x1 + 8 >= 8x1 + 8 = b(c(a(b(x1))))
        
        b(b(x1)) = 8x1 + 8 >= 8x1 + 8 = a(a(x1))
        
        a(c(x1)) = x1 + 4 >= x1 = x1
       problem:
        DPs:
         a#(a(x1)) -> a#(b(x1))
        TRS:
         a(a(x1)) -> b(c(a(b(x1))))
         b(b(x1)) -> a(a(x1))
         a(c(x1)) -> x1
       Restore Modifier:
        DPs:
         a#(a(x1)) -> a#(b(x1))
        TRS:
         a(a(x1)) -> b(c(a(b(x1))))
         b(b(x1)) -> a(a(x1))
         a(c(x1)) -> x1
        EDG Processor:
         DPs:
          a#(a(x1)) -> a#(b(x1))
         TRS:
          a(a(x1)) -> b(c(a(b(x1))))
          b(b(x1)) -> a(a(x1))
          a(c(x1)) -> x1
         graph:
          a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1))
         Arctic Interpretation Processor:
          dimension: 2
          usable rules:
           a(a(x1)) -> b(c(a(b(x1))))
           b(b(x1)) -> a(a(x1))
           a(c(x1)) -> x1
          interpretation:
                     [-& 2 ]     [3]
           [b](x0) = [-1 -&]x0 + [1],
           
           [a#](x0) = [-& -1]x0 + [0],
           
                     [-& 1 ]     [2]
           [a](x0) = [0  -&]x0 + [2],
           
                     [-& 0 ]     [2]
           [c](x0) = [-1 -&]x0 + [0]
          orientation:
           a#(a(x1)) = [-1 -&]x1 + [1] >= [-2 -&]x1 + [0] = a#(b(x1))
           
                      [1  -&]     [3]    [1  -&]     [3]                 
           a(a(x1)) = [-& 1 ]x1 + [2] >= [-& 1 ]x1 + [2] = b(c(a(b(x1))))
           
                      [1  -&]     [3]    [1  -&]     [3]           
           b(b(x1)) = [-& 1 ]x1 + [2] >= [-& 1 ]x1 + [2] = a(a(x1))
           
                           [2]           
           a(c(x1)) = x1 + [2] >= x1 = x1
          problem:
           DPs:
            
           TRS:
            a(a(x1)) -> b(c(a(b(x1))))
            b(b(x1)) -> a(a(x1))
            a(c(x1)) -> x1
          Qed