YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> a(c(b(x1)))
  c(x1) -> b(x1)
  c(c(x1)) -> c(a(x1))
  DP Processor:
   DPs:
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> c#(b(x1))
    b#(a(x1)) -> a#(c(b(x1)))
    c#(x1) -> b#(x1)
    c#(c(x1)) -> a#(x1)
    c#(c(x1)) -> c#(a(x1))
   TRS:
    a(x1) -> x1
    b(a(x1)) -> a(c(b(x1)))
    c(x1) -> b(x1)
    c(c(x1)) -> c(a(x1))
   TDG Processor:
    DPs:
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> c#(b(x1))
     b#(a(x1)) -> a#(c(b(x1)))
     c#(x1) -> b#(x1)
     c#(c(x1)) -> a#(x1)
     c#(c(x1)) -> c#(a(x1))
    TRS:
     a(x1) -> x1
     b(a(x1)) -> a(c(b(x1)))
     c(x1) -> b(x1)
     c(c(x1)) -> c(a(x1))
    graph:
     c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> c#(a(x1))
     c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(x1)
     c#(c(x1)) -> c#(a(x1)) -> c#(x1) -> b#(x1)
     c#(x1) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1)))
     c#(x1) -> b#(x1) -> b#(a(x1)) -> c#(b(x1))
     c#(x1) -> b#(x1) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(a(x1))
     b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
     b#(a(x1)) -> c#(b(x1)) -> c#(x1) -> b#(x1)
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(x1)))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 12/36
     DPs:
      c#(c(x1)) -> c#(a(x1))
      c#(x1) -> b#(x1)
      b#(a(x1)) -> b#(x1)
      b#(a(x1)) -> c#(b(x1))
     TRS:
      a(x1) -> x1
      b(a(x1)) -> a(c(b(x1)))
      c(x1) -> b(x1)
      c(c(x1)) -> c(a(x1))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       b(a(x1)) -> a(c(b(x1)))
       c(x1) -> b(x1)
       c(c(x1)) -> c(a(x1))
      interpretation:
       [b#](x0) = [0 0]x0 + [2],
       
                 [0  -&]     [-&]
       [b](x0) = [0  -&]x0 + [0 ],
       
       [c#](x0) = [0 0]x0 + [2],
       
                 [1 0]     [3]
       [a](x0) = [0 0]x0 + [0],
       
                 [0 0]     [2]
       [c](x0) = [1 1]x0 + [3]
      orientation:
       c#(c(x1)) = [1 1]x1 + [3] >= [1 0]x1 + [3] = c#(a(x1))
       
       c#(x1) = [0 0]x1 + [2] >= [0 0]x1 + [2] = b#(x1)
       
       b#(a(x1)) = [1 0]x1 + [3] >= [0 0]x1 + [2] = b#(x1)
       
       b#(a(x1)) = [1 0]x1 + [3] >= [0  -&]x1 + [2] = c#(b(x1))
       
               [1 0]     [3]           
       a(x1) = [0 0]x1 + [0] >= x1 = x1
       
                  [1 0]     [3]    [1  -&]     [3]              
       b(a(x1)) = [1 0]x1 + [3] >= [1  -&]x1 + [3] = a(c(b(x1)))
       
               [0 0]     [2]    [0  -&]     [-&]        
       c(x1) = [1 1]x1 + [3] >= [0  -&]x1 + [0 ] = b(x1)
       
                  [1 1]     [3]    [1 0]     [3]           
       c(c(x1)) = [2 2]x1 + [4] >= [2 1]x1 + [4] = c(a(x1))
      problem:
       DPs:
        c#(c(x1)) -> c#(a(x1))
        c#(x1) -> b#(x1)
        b#(a(x1)) -> b#(x1)
       TRS:
        a(x1) -> x1
        b(a(x1)) -> a(c(b(x1)))
        c(x1) -> b(x1)
        c(c(x1)) -> c(a(x1))
      Restore Modifier:
       DPs:
        c#(c(x1)) -> c#(a(x1))
        c#(x1) -> b#(x1)
        b#(a(x1)) -> b#(x1)
       TRS:
        a(x1) -> x1
        b(a(x1)) -> a(c(b(x1)))
        c(x1) -> b(x1)
        c(c(x1)) -> c(a(x1))
       EDG Processor:
        DPs:
         c#(c(x1)) -> c#(a(x1))
         c#(x1) -> b#(x1)
         b#(a(x1)) -> b#(x1)
        TRS:
         a(x1) -> x1
         b(a(x1)) -> a(c(b(x1)))
         c(x1) -> b(x1)
         c(c(x1)) -> c(a(x1))
        graph:
         c#(c(x1)) -> c#(a(x1)) -> c#(x1) -> b#(x1)
         c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> c#(a(x1))
         c#(x1) -> b#(x1) -> b#(a(x1)) -> b#(x1)
         b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
        SCC Processor:
         #sccs: 2
         #rules: 2
         #arcs: 4/9
         DPs:
          c#(c(x1)) -> c#(a(x1))
         TRS:
          a(x1) -> x1
          b(a(x1)) -> a(c(b(x1)))
          c(x1) -> b(x1)
          c(c(x1)) -> c(a(x1))
         Usable Rule Processor:
          DPs:
           c#(c(x1)) -> c#(a(x1))
          TRS:
           a(x1) -> x1
          Arctic Interpretation Processor:
           dimension: 1
           usable rules:
            a(x1) -> x1
           interpretation:
            [c#](x0) = 13x0 + 0,
            
            [a](x0) = 1x0 + 5,
            
            [c](x0) = 2x0 + 6
           orientation:
            c#(c(x1)) = 15x1 + 19 >= 14x1 + 18 = c#(a(x1))
            
            a(x1) = 1x1 + 5 >= x1 = x1
           problem:
            DPs:
             
            TRS:
             a(x1) -> x1
           Qed
         
         DPs:
          b#(a(x1)) -> b#(x1)
         TRS:
          a(x1) -> x1
          b(a(x1)) -> a(c(b(x1)))
          c(x1) -> b(x1)
          c(c(x1)) -> c(a(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