YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  a(a(x1)) -> a(b(c(b(a(x1)))))
  c(b(x1)) -> a(c(x1))
  DP Processor:
   DPs:
    a#(a(x1)) -> c#(b(a(x1)))
    a#(a(x1)) -> a#(b(c(b(a(x1)))))
    c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1))
   TRS:
    a(x1) -> x1
    a(a(x1)) -> a(b(c(b(a(x1)))))
    c(b(x1)) -> a(c(x1))
   TDG Processor:
    DPs:
     a#(a(x1)) -> c#(b(a(x1)))
     a#(a(x1)) -> a#(b(c(b(a(x1)))))
     c#(b(x1)) -> c#(x1)
     c#(b(x1)) -> a#(c(x1))
    TRS:
     a(x1) -> x1
     a(a(x1)) -> a(b(c(b(a(x1)))))
     c(b(x1)) -> a(c(x1))
    graph:
     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
     c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(c(b(a(x1)))))
     c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(a(x1)))
     a#(a(x1)) -> c#(b(a(x1))) -> c#(b(x1)) -> a#(c(x1))
     a#(a(x1)) -> c#(b(a(x1))) -> c#(b(x1)) -> c#(x1)
     a#(a(x1)) -> a#(b(c(b(a(x1))))) ->
     a#(a(x1)) -> a#(b(c(b(a(x1)))))
     a#(a(x1)) -> a#(b(c(b(a(x1))))) -> a#(a(x1)) -> c#(b(a(x1)))
    EDG Processor:
     DPs:
      a#(a(x1)) -> c#(b(a(x1)))
      a#(a(x1)) -> a#(b(c(b(a(x1)))))
      c#(b(x1)) -> c#(x1)
      c#(b(x1)) -> a#(c(x1))
     TRS:
      a(x1) -> x1
      a(a(x1)) -> a(b(c(b(a(x1)))))
      c(b(x1)) -> a(c(x1))
     graph:
      c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
      c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
      c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(a(x1)))
      c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(c(b(a(x1)))))
      a#(a(x1)) -> c#(b(a(x1))) -> c#(b(x1)) -> c#(x1)
      a#(a(x1)) -> c#(b(a(x1))) -> c#(b(x1)) -> a#(c(x1))
     SCC Processor:
      #sccs: 1
      #rules: 3
      #arcs: 6/16
      DPs:
       c#(b(x1)) -> c#(x1)
       c#(b(x1)) -> a#(c(x1))
       a#(a(x1)) -> c#(b(a(x1)))
      TRS:
       a(x1) -> x1
       a(a(x1)) -> a(b(c(b(a(x1)))))
       c(b(x1)) -> a(c(x1))
      Arctic Interpretation Processor:
       dimension: 2
       usable rules:
        a(x1) -> x1
        a(a(x1)) -> a(b(c(b(a(x1)))))
        c(b(x1)) -> a(c(x1))
       interpretation:
        [c#](x0) = [-& -1]x0 + [0],
        
        [a#](x0) = [-1 0 ]x0 + [0],
        
                  [-& 0 ]     [0]
        [c](x0) = [-1 -&]x0 + [1],
        
                  [0 1]     [1]
        [b](x0) = [0 1]x0 + [2],
        
                  [1 1]     [2]
        [a](x0) = [0 0]x0 + [1]
       orientation:
        c#(b(x1)) = [-1 0 ]x1 + [1] >= [-& -1]x1 + [0] = c#(x1)
        
        c#(b(x1)) = [-1 0 ]x1 + [1] >= [-1 -1]x1 + [1] = a#(c(x1))
        
        a#(a(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = c#(b(a(x1)))
        
                [1 1]     [2]           
        a(x1) = [0 0]x1 + [1] >= x1 = x1
        
                   [2 2]     [3]    [2 2]     [3]                    
        a(a(x1)) = [1 1]x1 + [2] >= [1 1]x1 + [2] = a(b(c(b(a(x1)))))
        
                   [0  1 ]     [2]    [0  1 ]     [2]           
        c(b(x1)) = [-1 0 ]x1 + [1] >= [-1 0 ]x1 + [1] = a(c(x1))
       problem:
        DPs:
         c#(b(x1)) -> a#(c(x1))
         a#(a(x1)) -> c#(b(a(x1)))
        TRS:
         a(x1) -> x1
         a(a(x1)) -> a(b(c(b(a(x1)))))
         c(b(x1)) -> a(c(x1))
       Restore Modifier:
        DPs:
         c#(b(x1)) -> a#(c(x1))
         a#(a(x1)) -> c#(b(a(x1)))
        TRS:
         a(x1) -> x1
         a(a(x1)) -> a(b(c(b(a(x1)))))
         c(b(x1)) -> a(c(x1))
        EDG Processor:
         DPs:
          c#(b(x1)) -> a#(c(x1))
          a#(a(x1)) -> c#(b(a(x1)))
         TRS:
          a(x1) -> x1
          a(a(x1)) -> a(b(c(b(a(x1)))))
          c(b(x1)) -> a(c(x1))
         graph:
          c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(a(x1)))
          a#(a(x1)) -> c#(b(a(x1))) -> c#(b(x1)) -> a#(c(x1))
         Arctic Interpretation Processor:
          dimension: 3
          usable rules:
           a(x1) -> x1
           a(a(x1)) -> a(b(c(b(a(x1)))))
           c(b(x1)) -> a(c(x1))
          interpretation:
           [c#](x0) = [0  -& 1 ]x0 + [0],
           
           [a#](x0) = [0 1 0]x0 + [0],
           
                     [0  -& -&]     [0]
           [c](x0) = [0  -& 0 ]x0 + [0]
                     [0  -& -&]     [0],
           
                     [0  -& 0 ]     [0]
           [b](x0) = [0  0  0 ]x0 + [0]
                     [1  0  1 ]     [1],
           
                     [0 0 0]     [0]
           [a](x0) = [1 1 1]x0 + [1]
                     [0 0 0]     [0]
          orientation:
           c#(b(x1)) = [2 1 2]x1 + [2] >= [1  -& 1 ]x1 + [1] = a#(c(x1))
           
           a#(a(x1)) = [2 2 2]x1 + [2] >= [2 2 2]x1 + [2] = c#(b(a(x1)))
           
                   [0 0 0]     [0]           
           a(x1) = [1 1 1]x1 + [1] >= x1 = x1
                   [0 0 0]     [0]           
           
                      [1 1 1]     [1]    [1 1 1]     [1]                    
           a(a(x1)) = [2 2 2]x1 + [2] >= [2 2 2]x1 + [2] = a(b(c(b(a(x1)))))
                      [1 1 1]     [1]    [1 1 1]     [1]                    
           
                      [0  -& 0 ]     [0]    [0  -& 0 ]     [0]           
           c(b(x1)) = [1  0  1 ]x1 + [1] >= [1  -& 1 ]x1 + [1] = a(c(x1))
                      [0  -& 0 ]     [0]    [0  -& 0 ]     [0]           
          problem:
           DPs:
            a#(a(x1)) -> c#(b(a(x1)))
           TRS:
            a(x1) -> x1
            a(a(x1)) -> a(b(c(b(a(x1)))))
            c(b(x1)) -> a(c(x1))
          Restore Modifier:
           DPs:
            a#(a(x1)) -> c#(b(a(x1)))
           TRS:
            a(x1) -> x1
            a(a(x1)) -> a(b(c(b(a(x1)))))
            c(b(x1)) -> a(c(x1))
           EDG Processor:
            DPs:
             a#(a(x1)) -> c#(b(a(x1)))
            TRS:
             a(x1) -> x1
             a(a(x1)) -> a(b(c(b(a(x1)))))
             c(b(x1)) -> a(c(x1))
            graph:
             
            Qed