YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(a(x1))) -> c(a(c(c(x1))))
  c(c(x1)) -> a(b(x1))
  DP Processor:
   DPs:
    b#(a(a(x1))) -> c#(x1)
    b#(a(a(x1))) -> c#(c(x1))
    b#(a(a(x1))) -> a#(c(c(x1)))
    b#(a(a(x1))) -> c#(a(c(c(x1))))
    c#(c(x1)) -> b#(x1)
    c#(c(x1)) -> a#(b(x1))
   TRS:
    a(x1) -> x1
    b(a(a(x1))) -> c(a(c(c(x1))))
    c(c(x1)) -> a(b(x1))
   TDG Processor:
    DPs:
     b#(a(a(x1))) -> c#(x1)
     b#(a(a(x1))) -> c#(c(x1))
     b#(a(a(x1))) -> a#(c(c(x1)))
     b#(a(a(x1))) -> c#(a(c(c(x1))))
     c#(c(x1)) -> b#(x1)
     c#(c(x1)) -> a#(b(x1))
    TRS:
     a(x1) -> x1
     b(a(a(x1))) -> c(a(c(c(x1))))
     c(c(x1)) -> a(b(x1))
    graph:
     c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(a(c(c(x1))))
     c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(c(c(x1)))
     c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(c(x1))
     c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(x1)
     b#(a(a(x1))) -> c#(c(x1)) -> c#(c(x1)) -> a#(b(x1))
     b#(a(a(x1))) -> c#(c(x1)) -> c#(c(x1)) -> b#(x1)
     b#(a(a(x1))) -> c#(a(c(c(x1)))) -> c#(c(x1)) -> a#(b(x1))
     b#(a(a(x1))) -> c#(a(c(c(x1)))) -> c#(c(x1)) -> b#(x1)
     b#(a(a(x1))) -> c#(x1) -> c#(c(x1)) -> a#(b(x1))
     b#(a(a(x1))) -> c#(x1) -> c#(c(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 10/36
     DPs:
      c#(c(x1)) -> b#(x1)
      b#(a(a(x1))) -> c#(x1)
      b#(a(a(x1))) -> c#(c(x1))
      b#(a(a(x1))) -> c#(a(c(c(x1))))
     TRS:
      a(x1) -> x1
      b(a(a(x1))) -> c(a(c(c(x1))))
      c(c(x1)) -> a(b(x1))
     Arctic Interpretation Processor:
      dimension: 3
      usable rules:
       a(x1) -> x1
       b(a(a(x1))) -> c(a(c(c(x1))))
       c(c(x1)) -> a(b(x1))
      interpretation:
       [c#](x0) = [0 0 0]x0,
       
       [b#](x0) = [-& 0  0 ]x0 + [0],
       
                 [0  0  1 ]     [0 ]
       [c](x0) = [-& 0  0 ]x0 + [-&]
                 [0  1  0 ]     [-&],
       
                 [0  1  -&]  
       [b](x0) = [-& 0  -&]x0
                 [0  1  -&]  ,
       
                 [0  0  0 ]     [-&]
       [a](x0) = [0  1  0 ]x0 + [-&]
                 [-& 0  0 ]     [0 ]
      orientation:
       c#(c(x1)) = [0 1 1]x1 + [0] >= [-& 0  0 ]x1 + [0] = b#(x1)
       
       b#(a(a(x1))) = [1 2 1]x1 + [0] >= [0 0 0]x1 = c#(x1)
       
       b#(a(a(x1))) = [1 2 1]x1 + [0] >= [0 1 1]x1 + [0] = c#(c(x1))
       
       b#(a(a(x1))) = [1 2 1]x1 + [0] >= [1 2 1]x1 + [0] = c#(a(c(c(x1))))
       
               [0  0  0 ]     [-&]           
       a(x1) = [0  1  0 ]x1 + [-&] >= x1 = x1
               [-& 0  0 ]     [0 ]           
       
                     [2 3 2]     [1]    [1 2 2]     [1]                 
       b(a(a(x1))) = [1 2 1]x1 + [0] >= [1 2 1]x1 + [0] = c(a(c(c(x1))))
                     [2 3 2]     [1]    [2 3 2]     [1]                 
       
                  [1 2 1]     [0 ]    [0  1  -&]     [-&]           
       c(c(x1)) = [0 1 0]x1 + [-&] >= [0  1  -&]x1 + [-&] = a(b(x1))
                  [0 1 1]     [0 ]    [0  1  -&]     [0 ]           
      problem:
       DPs:
        c#(c(x1)) -> b#(x1)
        b#(a(a(x1))) -> c#(c(x1))
        b#(a(a(x1))) -> c#(a(c(c(x1))))
       TRS:
        a(x1) -> x1
        b(a(a(x1))) -> c(a(c(c(x1))))
        c(c(x1)) -> a(b(x1))
      Restore Modifier:
       DPs:
        c#(c(x1)) -> b#(x1)
        b#(a(a(x1))) -> c#(c(x1))
        b#(a(a(x1))) -> c#(a(c(c(x1))))
       TRS:
        a(x1) -> x1
        b(a(a(x1))) -> c(a(c(c(x1))))
        c(c(x1)) -> a(b(x1))
       EDG Processor:
        DPs:
         c#(c(x1)) -> b#(x1)
         b#(a(a(x1))) -> c#(c(x1))
         b#(a(a(x1))) -> c#(a(c(c(x1))))
        TRS:
         a(x1) -> x1
         b(a(a(x1))) -> c(a(c(c(x1))))
         c(c(x1)) -> a(b(x1))
        graph:
         c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(c(x1))
         c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(a(c(c(x1))))
         b#(a(a(x1))) -> c#(c(x1)) -> c#(c(x1)) -> b#(x1)
         b#(a(a(x1))) -> c#(a(c(c(x1)))) -> c#(c(x1)) -> b#(x1)
        Arctic Interpretation Processor:
         dimension: 2
         usable rules:
          a(x1) -> x1
          b(a(a(x1))) -> c(a(c(c(x1))))
          c(c(x1)) -> a(b(x1))
         interpretation:
          [c#](x0) = [0 2]x0,
          
          [b#](x0) = [3 0]x0,
          
                    [0 0]  
          [c](x0) = [1 0]x0,
          
                    [0  -&]  
          [b](x0) = [1  0 ]x0,
          
                    [1 0]  
          [a](x0) = [0 0]x0
         orientation:
          c#(c(x1)) = [3 2]x1 >= [3 0]x1 = b#(x1)
          
          b#(a(a(x1))) = [5 4]x1 >= [3 2]x1 = c#(c(x1))
          
          b#(a(a(x1))) = [5 4]x1 >= [3 3]x1 = c#(a(c(c(x1))))
          
                  [1 0]             
          a(x1) = [0 0]x1 >= x1 = x1
          
                        [2 1]      [2 1]                   
          b(a(a(x1))) = [3 2]x1 >= [3 2]x1 = c(a(c(c(x1))))
          
                     [1 0]      [1 0]             
          c(c(x1)) = [1 1]x1 >= [1 0]x1 = a(b(x1))
         problem:
          DPs:
           c#(c(x1)) -> b#(x1)
          TRS:
           a(x1) -> x1
           b(a(a(x1))) -> c(a(c(c(x1))))
           c(c(x1)) -> a(b(x1))
         Restore Modifier:
          DPs:
           c#(c(x1)) -> b#(x1)
          TRS:
           a(x1) -> x1
           b(a(a(x1))) -> c(a(c(c(x1))))
           c(c(x1)) -> a(b(x1))
          EDG Processor:
           DPs:
            c#(c(x1)) -> b#(x1)
           TRS:
            a(x1) -> x1
            b(a(a(x1))) -> c(a(c(c(x1))))
            c(c(x1)) -> a(b(x1))
           graph:
            
           Qed