YES

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

Proof:
 String Reversal Processor:
  a(x1) -> b(x1)
  c(a(b(x1))) -> a(a(b(c(x1))))
  b(b(x1)) -> c(x1)
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    c#(a(b(x1))) -> c#(x1)
    c#(a(b(x1))) -> b#(c(x1))
    c#(a(b(x1))) -> a#(b(c(x1)))
    c#(a(b(x1))) -> a#(a(b(c(x1))))
    b#(b(x1)) -> c#(x1)
   TRS:
    a(x1) -> b(x1)
    c(a(b(x1))) -> a(a(b(c(x1))))
    b(b(x1)) -> c(x1)
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     c#(a(b(x1))) -> c#(x1)
     c#(a(b(x1))) -> b#(c(x1))
     c#(a(b(x1))) -> a#(b(c(x1)))
     c#(a(b(x1))) -> a#(a(b(c(x1))))
     b#(b(x1)) -> c#(x1)
    TRS:
     a(x1) -> b(x1)
     c(a(b(x1))) -> a(a(b(c(x1))))
     b(b(x1)) -> c(x1)
    graph:
     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> a#(a(b(c(x1))))
     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> a#(b(c(x1)))
     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> b#(c(x1))
     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> c#(x1)
     c#(a(b(x1))) -> b#(c(x1)) -> b#(b(x1)) -> c#(x1)
     c#(a(b(x1))) -> a#(b(c(x1))) -> a#(x1) -> b#(x1)
     c#(a(b(x1))) -> a#(a(b(c(x1)))) -> a#(x1) -> b#(x1)
     b#(b(x1)) -> c#(x1) -> c#(a(b(x1))) -> a#(a(b(c(x1))))
     b#(b(x1)) -> c#(x1) -> c#(a(b(x1))) -> a#(b(c(x1)))
     b#(b(x1)) -> c#(x1) -> c#(a(b(x1))) -> b#(c(x1))
     b#(b(x1)) -> c#(x1) -> c#(a(b(x1))) -> c#(x1)
     a#(x1) -> b#(x1) -> b#(b(x1)) -> c#(x1)
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> b(x1)
      c(a(b(x1))) -> a(a(b(c(x1))))
      b(b(x1)) -> c(x1)
     interpretation:
      [b#](x0) = [0 0]x0 + [0],
      
                [-& 0 ]     [2]
      [b](x0) = [0  0 ]x0 + [3],
      
      [a#](x0) = [0 3]x0 + [0],
      
      [c#](x0) = [0 0]x0 + [0],
      
                [-& 3 ]     [2]
      [a](x0) = [0  0 ]x0 + [3],
      
                [0  -&]     [-&]
      [c](x0) = [0  -&]x0 + [0 ]
     orientation:
      a#(x1) = [0 3]x1 + [0] >= [0 0]x1 + [0] = b#(x1)
      
      c#(a(b(x1))) = [3 3]x1 + [6] >= [0 0]x1 + [0] = c#(x1)
      
      c#(a(b(x1))) = [3 3]x1 + [6] >= [0  -&]x1 + [0] = b#(c(x1))
      
      c#(a(b(x1))) = [3 3]x1 + [6] >= [3  -&]x1 + [6] = a#(b(c(x1)))
      
      c#(a(b(x1))) = [3 3]x1 + [6] >= [3  -&]x1 + [6] = a#(a(b(c(x1))))
      
      b#(b(x1)) = [0 0]x1 + [3] >= [0 0]x1 + [0] = c#(x1)
      
              [-& 3 ]     [2]    [-& 0 ]     [2]        
      a(x1) = [0  0 ]x1 + [3] >= [0  0 ]x1 + [3] = b(x1)
      
                    [3 3]     [6]    [3  -&]     [6]                 
      c(a(b(x1))) = [3 3]x1 + [6] >= [3  -&]x1 + [6] = a(a(b(c(x1))))
      
                 [0 0]     [3]    [0  -&]     [-&]        
      b(b(x1)) = [0 0]x1 + [3] >= [0  -&]x1 + [0 ] = c(x1)
     problem:
      DPs:
       a#(x1) -> b#(x1)
       c#(a(b(x1))) -> a#(b(c(x1)))
       c#(a(b(x1))) -> a#(a(b(c(x1))))
       b#(b(x1)) -> c#(x1)
      TRS:
       a(x1) -> b(x1)
       c(a(b(x1))) -> a(a(b(c(x1))))
       b(b(x1)) -> c(x1)
     Restore Modifier:
      DPs:
       a#(x1) -> b#(x1)
       c#(a(b(x1))) -> a#(b(c(x1)))
       c#(a(b(x1))) -> a#(a(b(c(x1))))
       b#(b(x1)) -> c#(x1)
      TRS:
       a(x1) -> b(x1)
       c(a(b(x1))) -> a(a(b(c(x1))))
       b(b(x1)) -> c(x1)
      EDG Processor:
       DPs:
        a#(x1) -> b#(x1)
        c#(a(b(x1))) -> a#(b(c(x1)))
        c#(a(b(x1))) -> a#(a(b(c(x1))))
        b#(b(x1)) -> c#(x1)
       TRS:
        a(x1) -> b(x1)
        c(a(b(x1))) -> a(a(b(c(x1))))
        b(b(x1)) -> c(x1)
       graph:
        c#(a(b(x1))) -> a#(b(c(x1))) -> a#(x1) -> b#(x1)
        c#(a(b(x1))) -> a#(a(b(c(x1)))) -> a#(x1) -> b#(x1)
        b#(b(x1)) -> c#(x1) -> c#(a(b(x1))) -> a#(b(c(x1)))
        b#(b(x1)) -> c#(x1) -> c#(a(b(x1))) -> a#(a(b(c(x1))))
        a#(x1) -> b#(x1) -> b#(b(x1)) -> c#(x1)
       Arctic Interpretation Processor:
        dimension: 2
        usable rules:
         a(x1) -> b(x1)
         c(a(b(x1))) -> a(a(b(c(x1))))
         b(b(x1)) -> c(x1)
        interpretation:
         [b#](x0) = [-& 0 ]x0 + [3],
         
                   [0  -&]     [0]
         [b](x0) = [1  -&]x0 + [2],
         
         [a#](x0) = [-& 2 ]x0 + [3],
         
         [c#](x0) = [0  -&]x0 + [0],
         
                   [0  2 ]     [0]
         [a](x0) = [1  -&]x0 + [2],
         
                   [0  -&]     [0]
         [c](x0) = [1  -&]x0 + [2]
        orientation:
         a#(x1) = [-& 2 ]x1 + [3] >= [-& 0 ]x1 + [3] = b#(x1)
         
         c#(a(b(x1))) = [3  -&]x1 + [4] >= [3  -&]x1 + [4] = a#(b(c(x1)))
         
         c#(a(b(x1))) = [3  -&]x1 + [4] >= [3  -&]x1 + [4] = a#(a(b(c(x1))))
         
         b#(b(x1)) = [1  -&]x1 + [3] >= [0  -&]x1 + [0] = c#(x1)
         
                 [0  2 ]     [0]    [0  -&]     [0]        
         a(x1) = [1  -&]x1 + [2] >= [1  -&]x1 + [2] = b(x1)
         
                       [3  -&]     [4]    [3  -&]     [4]                 
         c(a(b(x1))) = [4  -&]x1 + [5] >= [4  -&]x1 + [5] = a(a(b(c(x1))))
         
                    [0  -&]     [0]    [0  -&]     [0]        
         b(b(x1)) = [1  -&]x1 + [2] >= [1  -&]x1 + [2] = c(x1)
        problem:
         DPs:
          a#(x1) -> b#(x1)
          c#(a(b(x1))) -> a#(b(c(x1)))
          c#(a(b(x1))) -> a#(a(b(c(x1))))
         TRS:
          a(x1) -> b(x1)
          c(a(b(x1))) -> a(a(b(c(x1))))
          b(b(x1)) -> c(x1)
        Restore Modifier:
         DPs:
          a#(x1) -> b#(x1)
          c#(a(b(x1))) -> a#(b(c(x1)))
          c#(a(b(x1))) -> a#(a(b(c(x1))))
         TRS:
          a(x1) -> b(x1)
          c(a(b(x1))) -> a(a(b(c(x1))))
          b(b(x1)) -> c(x1)
         EDG Processor:
          DPs:
           a#(x1) -> b#(x1)
           c#(a(b(x1))) -> a#(b(c(x1)))
           c#(a(b(x1))) -> a#(a(b(c(x1))))
          TRS:
           a(x1) -> b(x1)
           c(a(b(x1))) -> a(a(b(c(x1))))
           b(b(x1)) -> c(x1)
          graph:
           c#(a(b(x1))) -> a#(b(c(x1))) -> a#(x1) -> b#(x1)
           c#(a(b(x1))) -> a#(a(b(c(x1)))) -> a#(x1) -> b#(x1)
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 2/9