YES

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

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