YES

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

Proof:
 String Reversal Processor:
  a(x1) -> b(x1)
  b(b(a(x1))) -> c(x1)
  c(a(x1)) -> a(a(b(c(x1))))
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    b#(b(a(x1))) -> c#(x1)
    c#(a(x1)) -> c#(x1)
    c#(a(x1)) -> b#(c(x1))
    c#(a(x1)) -> a#(b(c(x1)))
    c#(a(x1)) -> a#(a(b(c(x1))))
   TRS:
    a(x1) -> b(x1)
    b(b(a(x1))) -> c(x1)
    c(a(x1)) -> a(a(b(c(x1))))
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     b#(b(a(x1))) -> c#(x1)
     c#(a(x1)) -> c#(x1)
     c#(a(x1)) -> b#(c(x1))
     c#(a(x1)) -> a#(b(c(x1)))
     c#(a(x1)) -> a#(a(b(c(x1))))
    TRS:
     a(x1) -> b(x1)
     b(b(a(x1))) -> c(x1)
     c(a(x1)) -> a(a(b(c(x1))))
    graph:
     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(a(b(c(x1))))
     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(b(c(x1)))
     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(c(x1))
     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
     c#(a(x1)) -> b#(c(x1)) -> b#(b(a(x1))) -> c#(x1)
     c#(a(x1)) -> a#(b(c(x1))) -> a#(x1) -> b#(x1)
     c#(a(x1)) -> a#(a(b(c(x1)))) -> a#(x1) -> b#(x1)
     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(a(b(c(x1))))
     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(b(c(x1)))
     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> b#(c(x1))
     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1)
     a#(x1) -> b#(x1) -> b#(b(a(x1))) -> c#(x1)
    Arctic Interpretation Processor:
     dimension: 3
     usable rules:
      a(x1) -> b(x1)
      b(b(a(x1))) -> c(x1)
      c(a(x1)) -> a(a(b(c(x1))))
     interpretation:
      [b#](x0) = [-& -& 0 ]x0 + [0],
      
                [0  0  0 ]  
      [b](x0) = [0  0  0 ]x0
                [-& 0  -&]  ,
      
      [a#](x0) = [-& -& 0 ]x0 + [0],
      
      [c#](x0) = [0 0 0]x0 + [0],
      
                [0 0 1]     [-&]
      [a](x0) = [0 0 0]x0 + [-&]
                [0 0 1]     [1 ],
      
                [0  0  1 ]  
      [c](x0) = [-& -& 0 ]x0
                [0  0  1 ]  
     orientation:
      a#(x1) = [-& -& 0 ]x1 + [0] >= [-& -& 0 ]x1 + [0] = b#(x1)
      
      b#(b(a(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c#(x1)
      
      c#(a(x1)) = [0 0 1]x1 + [1] >= [0 0 0]x1 + [0] = c#(x1)
      
      c#(a(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [0] = b#(c(x1))
      
      c#(a(x1)) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = a#(b(c(x1)))
      
      c#(a(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = a#(a(b(c(x1))))
      
              [0 0 1]     [-&]    [0  0  0 ]          
      a(x1) = [0 0 0]x1 + [-&] >= [0  0  0 ]x1 = b(x1)
              [0 0 1]     [1 ]    [-& 0  -&]          
      
                    [0 0 1]     [1]    [0  0  1 ]          
      b(b(a(x1))) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 = c(x1)
                    [0 0 1]     [1]    [0  0  1 ]          
      
                 [1 1 2]     [2]    [1 1 2]     [2]                 
      c(a(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = a(a(b(c(x1))))
                 [1 1 2]     [2]    [1 1 2]     [2]                 
     problem:
      DPs:
       a#(x1) -> b#(x1)
       b#(b(a(x1))) -> c#(x1)
       c#(a(x1)) -> c#(x1)
       c#(a(x1)) -> b#(c(x1))
       c#(a(x1)) -> a#(a(b(c(x1))))
      TRS:
       a(x1) -> b(x1)
       b(b(a(x1))) -> c(x1)
       c(a(x1)) -> a(a(b(c(x1))))
     Restore Modifier:
      DPs:
       a#(x1) -> b#(x1)
       b#(b(a(x1))) -> c#(x1)
       c#(a(x1)) -> c#(x1)
       c#(a(x1)) -> b#(c(x1))
       c#(a(x1)) -> a#(a(b(c(x1))))
      TRS:
       a(x1) -> b(x1)
       b(b(a(x1))) -> c(x1)
       c(a(x1)) -> a(a(b(c(x1))))
      EDG Processor:
       DPs:
        a#(x1) -> b#(x1)
        b#(b(a(x1))) -> c#(x1)
        c#(a(x1)) -> c#(x1)
        c#(a(x1)) -> b#(c(x1))
        c#(a(x1)) -> a#(a(b(c(x1))))
       TRS:
        a(x1) -> b(x1)
        b(b(a(x1))) -> c(x1)
        c(a(x1)) -> a(a(b(c(x1))))
       graph:
        c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
        c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(c(x1))
        c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(a(b(c(x1))))
        c#(a(x1)) -> b#(c(x1)) -> b#(b(a(x1))) -> c#(x1)
        c#(a(x1)) -> a#(a(b(c(x1)))) -> a#(x1) -> b#(x1)
        b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1)
        b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> b#(c(x1))
        b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(a(b(c(x1))))
        a#(x1) -> b#(x1) -> b#(b(a(x1))) -> c#(x1)
       Arctic Interpretation Processor:
        dimension: 2
        usable rules:
         a(x1) -> b(x1)
         b(b(a(x1))) -> c(x1)
         c(a(x1)) -> a(a(b(c(x1))))
        interpretation:
         [b#](x0) = [0 0]x0 + [0],
         
                   [0  0 ]  
         [b](x0) = [0  -&]x0,
         
         [a#](x0) = [0 0]x0 + [0],
         
         [c#](x0) = [0 1]x0 + [0],
         
                   [0 0]     [0]
         [a](x0) = [0 3]x0 + [3],
         
                   [-& 0 ]     [0]
         [c](x0) = [0  3 ]x0 + [2]
        orientation:
         a#(x1) = [0 0]x1 + [0] >= [0 0]x1 + [0] = b#(x1)
         
         b#(b(a(x1))) = [0 3]x1 + [3] >= [0 1]x1 + [0] = c#(x1)
         
         c#(a(x1)) = [1 4]x1 + [4] >= [0 1]x1 + [0] = c#(x1)
         
         c#(a(x1)) = [1 4]x1 + [4] >= [0 3]x1 + [2] = b#(c(x1))
         
         c#(a(x1)) = [1 4]x1 + [4] >= [0 3]x1 + [3] = a#(a(b(c(x1))))
         
                 [0 0]     [0]    [0  0 ]          
         a(x1) = [0 3]x1 + [3] >= [0  -&]x1 = b(x1)
         
                       [0 3]     [3]    [-& 0 ]     [0]        
         b(b(a(x1))) = [0 3]x1 + [3] >= [0  3 ]x1 + [2] = c(x1)
         
                    [0 3]     [3]    [0 3]     [3]                 
         c(a(x1)) = [3 6]x1 + [6] >= [3 6]x1 + [6] = a(a(b(c(x1))))
        problem:
         DPs:
          a#(x1) -> b#(x1)
          b#(b(a(x1))) -> c#(x1)
         TRS:
          a(x1) -> b(x1)
          b(b(a(x1))) -> c(x1)
          c(a(x1)) -> a(a(b(c(x1))))
        Restore Modifier:
         DPs:
          a#(x1) -> b#(x1)
          b#(b(a(x1))) -> c#(x1)
         TRS:
          a(x1) -> b(x1)
          b(b(a(x1))) -> c(x1)
          c(a(x1)) -> a(a(b(c(x1))))
         EDG Processor:
          DPs:
           a#(x1) -> b#(x1)
           b#(b(a(x1))) -> c#(x1)
          TRS:
           a(x1) -> b(x1)
           b(b(a(x1))) -> c(x1)
           c(a(x1)) -> a(a(b(c(x1))))
          graph:
           a#(x1) -> b#(x1) -> b#(b(a(x1))) -> c#(x1)
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 1/4