YES

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

Proof:
 String Reversal Processor:
  a(x1) -> c(b(x1))
  b(a(b(x1))) -> a(a(a(x1)))
  c(c(x1)) -> a(x1)
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(x1) -> c#(b(x1))
    b#(a(b(x1))) -> a#(x1)
    b#(a(b(x1))) -> a#(a(x1))
    b#(a(b(x1))) -> a#(a(a(x1)))
    c#(c(x1)) -> a#(x1)
   TRS:
    a(x1) -> c(b(x1))
    b(a(b(x1))) -> a(a(a(x1)))
    c(c(x1)) -> a(x1)
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     a#(x1) -> c#(b(x1))
     b#(a(b(x1))) -> a#(x1)
     b#(a(b(x1))) -> a#(a(x1))
     b#(a(b(x1))) -> a#(a(a(x1)))
     c#(c(x1)) -> a#(x1)
    TRS:
     a(x1) -> c(b(x1))
     b(a(b(x1))) -> a(a(a(x1)))
     c(c(x1)) -> a(x1)
    graph:
     c#(c(x1)) -> a#(x1) -> a#(x1) -> c#(b(x1))
     c#(c(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
     b#(a(b(x1))) -> a#(a(a(x1))) -> a#(x1) -> c#(b(x1))
     b#(a(b(x1))) -> a#(a(a(x1))) -> a#(x1) -> b#(x1)
     b#(a(b(x1))) -> a#(a(x1)) -> a#(x1) -> c#(b(x1))
     b#(a(b(x1))) -> a#(a(x1)) -> a#(x1) -> b#(x1)
     b#(a(b(x1))) -> a#(x1) -> a#(x1) -> c#(b(x1))
     b#(a(b(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
     a#(x1) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
     a#(x1) -> b#(x1) -> b#(a(b(x1))) -> a#(a(a(x1)))
     a#(x1) -> b#(x1) -> b#(a(b(x1))) -> a#(a(x1))
     a#(x1) -> b#(x1) -> b#(a(b(x1))) -> a#(x1)
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> c(b(x1))
      b(a(b(x1))) -> a(a(a(x1)))
      c(c(x1)) -> a(x1)
     interpretation:
      [c#](x0) = [-& 0 ]x0 + [0],
      
      [b#](x0) = [0  -&]x0 + [1],
      
      [a#](x0) = [0  -&]x0 + [1],
      
                [1  0 ]     [2]
      [b](x0) = [0  -&]x0 + [1],
      
                [-& 0 ]     [0]
      [c](x0) = [0  1 ]x0 + [1],
      
                [0  -&]     [1]
      [a](x0) = [1  0 ]x0 + [2]
     orientation:
      a#(x1) = [0  -&]x1 + [1] >= [0  -&]x1 + [1] = b#(x1)
      
      a#(x1) = [0  -&]x1 + [1] >= [0  -&]x1 + [1] = c#(b(x1))
      
      b#(a(b(x1))) = [1 0]x1 + [2] >= [0  -&]x1 + [1] = a#(x1)
      
      b#(a(b(x1))) = [1 0]x1 + [2] >= [0  -&]x1 + [1] = a#(a(x1))
      
      b#(a(b(x1))) = [1 0]x1 + [2] >= [0  -&]x1 + [1] = a#(a(a(x1)))
      
      c#(c(x1)) = [0 1]x1 + [1] >= [0  -&]x1 + [1] = a#(x1)
      
              [0  -&]     [1]    [0  -&]     [1]           
      a(x1) = [1  0 ]x1 + [2] >= [1  0 ]x1 + [2] = c(b(x1))
      
                    [2 1]     [3]    [0  -&]     [1]              
      b(a(b(x1))) = [1 0]x1 + [2] >= [1  0 ]x1 + [2] = a(a(a(x1)))
      
                 [0 1]     [1]    [0  -&]     [1]        
      c(c(x1)) = [1 2]x1 + [2] >= [1  0 ]x1 + [2] = a(x1)
     problem:
      DPs:
       a#(x1) -> b#(x1)
       a#(x1) -> c#(b(x1))
       c#(c(x1)) -> a#(x1)
      TRS:
       a(x1) -> c(b(x1))
       b(a(b(x1))) -> a(a(a(x1)))
       c(c(x1)) -> a(x1)
     Restore Modifier:
      DPs:
       a#(x1) -> b#(x1)
       a#(x1) -> c#(b(x1))
       c#(c(x1)) -> a#(x1)
      TRS:
       a(x1) -> c(b(x1))
       b(a(b(x1))) -> a(a(a(x1)))
       c(c(x1)) -> a(x1)
      EDG Processor:
       DPs:
        a#(x1) -> b#(x1)
        a#(x1) -> c#(b(x1))
        c#(c(x1)) -> a#(x1)
       TRS:
        a(x1) -> c(b(x1))
        b(a(b(x1))) -> a(a(a(x1)))
        c(c(x1)) -> a(x1)
       graph:
        c#(c(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
        c#(c(x1)) -> a#(x1) -> a#(x1) -> c#(b(x1))
        a#(x1) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
       SCC Processor:
        #sccs: 1
        #rules: 2
        #arcs: 3/9
        DPs:
         c#(c(x1)) -> a#(x1)
         a#(x1) -> c#(b(x1))
        TRS:
         a(x1) -> c(b(x1))
         b(a(b(x1))) -> a(a(a(x1)))
         c(c(x1)) -> a(x1)
        Arctic Interpretation Processor:
         dimension: 3
         usable rules:
          a(x1) -> c(b(x1))
          b(a(b(x1))) -> a(a(a(x1)))
          c(c(x1)) -> a(x1)
         interpretation:
          [c#](x0) = [0  0  -&]x0 + [0],
          
          [a#](x0) = [-& 1  -&]x0 + [1],
          
                    [-& 0  -&]     [0]
          [b](x0) = [-& 0  -&]x0 + [0]
                    [0  1  1 ]     [1],
          
                    [1  1  0 ]     [1]
          [c](x0) = [0  0  -&]x0 + [0]
                    [0  0  -&]     [0],
          
                    [0  1  1 ]     [1]
          [a](x0) = [-& 0  0 ]x0 + [0]
                    [-& 0  0 ]     [0]
         orientation:
          c#(c(x1)) = [1 1 0]x1 + [1] >= [-& 1  -&]x1 + [1] = a#(x1)
          
          a#(x1) = [-& 1  -&]x1 + [1] >= [-& 0  -&]x1 + [0] = c#(b(x1))
          
                  [0  1  1 ]     [1]    [0  1  1 ]     [1]           
          a(x1) = [-& 0  0 ]x1 + [0] >= [-& 0  -&]x1 + [0] = c(b(x1))
                  [-& 0  0 ]     [0]    [-& 0  -&]     [0]           
          
                        [0 1 1]     [1]    [0  1  1 ]     [1]              
          b(a(b(x1))) = [0 1 1]x1 + [1] >= [-& 0  0 ]x1 + [0] = a(a(a(x1)))
                        [1 2 2]     [2]    [-& 0  0 ]     [0]              
          
                     [2 2 1]     [2]    [0  1  1 ]     [1]        
          c(c(x1)) = [1 1 0]x1 + [1] >= [-& 0  0 ]x1 + [0] = a(x1)
                     [1 1 0]     [1]    [-& 0  0 ]     [0]        
         problem:
          DPs:
           c#(c(x1)) -> a#(x1)
          TRS:
           a(x1) -> c(b(x1))
           b(a(b(x1))) -> a(a(a(x1)))
           c(c(x1)) -> a(x1)
         Restore Modifier:
          DPs:
           c#(c(x1)) -> a#(x1)
          TRS:
           a(x1) -> c(b(x1))
           b(a(b(x1))) -> a(a(a(x1)))
           c(c(x1)) -> a(x1)
          EDG Processor:
           DPs:
            c#(c(x1)) -> a#(x1)
           TRS:
            a(x1) -> c(b(x1))
            b(a(b(x1))) -> a(a(a(x1)))
            c(c(x1)) -> a(x1)
           graph:
            
           Qed