YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> c(a(b(x1)))
  b(b(x1)) -> x1
  c(c(x1)) -> a(b(x1))
  DP Processor:
   DPs:
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> a#(b(x1))
    b#(a(x1)) -> c#(a(b(x1)))
    c#(c(x1)) -> b#(x1)
    c#(c(x1)) -> a#(b(x1))
   TRS:
    a(x1) -> x1
    b(a(x1)) -> c(a(b(x1)))
    b(b(x1)) -> x1
    c(c(x1)) -> a(b(x1))
   TDG Processor:
    DPs:
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> a#(b(x1))
     b#(a(x1)) -> c#(a(b(x1)))
     c#(c(x1)) -> b#(x1)
     c#(c(x1)) -> a#(b(x1))
    TRS:
     a(x1) -> x1
     b(a(x1)) -> c(a(b(x1)))
     b(b(x1)) -> x1
     c(c(x1)) -> a(b(x1))
    graph:
     c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1)))
     c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
     c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> a#(b(x1))
     b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> b#(x1)
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1)))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 8/25
     DPs:
      c#(c(x1)) -> b#(x1)
      b#(a(x1)) -> b#(x1)
      b#(a(x1)) -> c#(a(b(x1)))
     TRS:
      a(x1) -> x1
      b(a(x1)) -> c(a(b(x1)))
      b(b(x1)) -> x1
      c(c(x1)) -> a(b(x1))
     Arctic Interpretation Processor:
      dimension: 4
      usable rules:
       a(x1) -> x1
       b(a(x1)) -> c(a(b(x1)))
       b(b(x1)) -> x1
       c(c(x1)) -> a(b(x1))
      interpretation:
       [c#](x0) = [0  -& -& 0 ]x0 + [0],
       
       [b#](x0) = [0  0  -& 0 ]x0,
       
                 [0  0  0  0 ]     [0 ]
                 [1  0  0  0 ]     [-&]
       [c](x0) = [1  0  -& 0 ]x0 + [0 ]
                 [1  0  0  0 ]     [1 ],
       
                 [0  0  0  0 ]  
                 [0  0  0  0 ]  
       [b](x0) = [0  0  0  -&]x0
                 [0  0  0  0 ]  ,
       
                 [0  0  -& 0 ]     [-&]
                 [1  1  1  0 ]     [0 ]
       [a](x0) = [0  1  0  1 ]x0 + [1 ]
                 [-& 0  0  1 ]     [-&]
      orientation:
       c#(c(x1)) = [1 0 0 0]x1 + [1] >= [0  0  -& 0 ]x1 = b#(x1)
       
       b#(a(x1)) = [1 1 1 1]x1 + [0] >= [0  0  -& 0 ]x1 = b#(x1)
       
       b#(a(x1)) = [1 1 1 1]x1 + [0] >= [1 1 1 1]x1 + [0] = c#(a(b(x1)))
       
               [0  0  -& 0 ]     [-&]           
               [1  1  1  0 ]     [0 ]           
       a(x1) = [0  1  0  1 ]x1 + [1 ] >= x1 = x1
               [-& 0  0  1 ]     [-&]           
       
                  [1 1 1 1]     [1]    [1 1 1 1]     [1]              
                  [1 1 1 1]     [1]    [1 1 1 1]     [1]              
       b(a(x1)) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [0] = c(a(b(x1)))
                  [1 1 1 1]     [1]    [1 1 1 1]     [1]              
       
                  [0 0 0 0]             
                  [0 0 0 0]             
       b(b(x1)) = [0 0 0 0]x1 >= x1 = x1
                  [0 0 0 0]             
       
                  [1 0 0 0]     [1]    [0 0 0 0]     [-&]           
                  [1 1 1 1]     [1]    [1 1 1 1]     [0 ]           
       c(c(x1)) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [1 ] = a(b(x1))
                  [1 1 1 1]     [1]    [1 1 1 1]     [-&]           
      problem:
       DPs:
        c#(c(x1)) -> b#(x1)
        b#(a(x1)) -> c#(a(b(x1)))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> c(a(b(x1)))
        b(b(x1)) -> x1
        c(c(x1)) -> a(b(x1))
      Restore Modifier:
       DPs:
        c#(c(x1)) -> b#(x1)
        b#(a(x1)) -> c#(a(b(x1)))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> c(a(b(x1)))
        b(b(x1)) -> x1
        c(c(x1)) -> a(b(x1))
       EDG Processor:
        DPs:
         c#(c(x1)) -> b#(x1)
         b#(a(x1)) -> c#(a(b(x1)))
        TRS:
         a(x1) -> x1
         b(a(x1)) -> c(a(b(x1)))
         b(b(x1)) -> x1
         c(c(x1)) -> a(b(x1))
        graph:
         c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1)))
         b#(a(x1)) -> c#(a(b(x1))) -> c#(c(x1)) -> b#(x1)
        Arctic Interpretation Processor:
         dimension: 2
         usable rules:
          a(x1) -> x1
          b(a(x1)) -> c(a(b(x1)))
          b(b(x1)) -> x1
          c(c(x1)) -> a(b(x1))
         interpretation:
          [c#](x0) = [-& 0 ]x0 + [0],
          
          [b#](x0) = [0 0]x0 + [0],
          
                    [-& 1 ]     [1 ]
          [c](x0) = [0  0 ]x0 + [-&],
          
                    [0 0]     [0 ]
          [b](x0) = [0 0]x0 + [-&],
          
                    [1 1]     [1]
          [a](x0) = [0 0]x0 + [0]
         orientation:
          c#(c(x1)) = [0 0]x1 + [0] >= [0 0]x1 + [0] = b#(x1)
          
          b#(a(x1)) = [1 1]x1 + [1] >= [0 0]x1 + [0] = c#(a(b(x1)))
          
                  [1 1]     [1]           
          a(x1) = [0 0]x1 + [0] >= x1 = x1
          
                     [1 1]     [1]    [1 1]     [1]              
          b(a(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = c(a(b(x1)))
          
                     [0 0]     [0]           
          b(b(x1)) = [0 0]x1 + [0] >= x1 = x1
          
                     [1 1]     [1]    [1 1]     [1]           
          c(c(x1)) = [0 1]x1 + [1] >= [0 0]x1 + [0] = a(b(x1))
         problem:
          DPs:
           c#(c(x1)) -> b#(x1)
          TRS:
           a(x1) -> x1
           b(a(x1)) -> c(a(b(x1)))
           b(b(x1)) -> x1
           c(c(x1)) -> a(b(x1))
         Restore Modifier:
          DPs:
           c#(c(x1)) -> b#(x1)
          TRS:
           a(x1) -> x1
           b(a(x1)) -> c(a(b(x1)))
           b(b(x1)) -> x1
           c(c(x1)) -> a(b(x1))
          EDG Processor:
           DPs:
            c#(c(x1)) -> b#(x1)
           TRS:
            a(x1) -> x1
            b(a(x1)) -> c(a(b(x1)))
            b(b(x1)) -> x1
            c(c(x1)) -> a(b(x1))
           graph:
            
           Qed