YES

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

Proof:
 String Reversal Processor:
  b(a(x1)) -> x1
  c(a(x1)) -> a(c(c(b(x1))))
  c(b(x1)) -> b(a(x1))
  DP Processor:
   DPs:
    c#(a(x1)) -> b#(x1)
    c#(a(x1)) -> c#(b(x1))
    c#(a(x1)) -> c#(c(b(x1)))
    c#(b(x1)) -> b#(a(x1))
   TRS:
    b(a(x1)) -> x1
    c(a(x1)) -> a(c(c(b(x1))))
    c(b(x1)) -> b(a(x1))
   TDG Processor:
    DPs:
     c#(a(x1)) -> b#(x1)
     c#(a(x1)) -> c#(b(x1))
     c#(a(x1)) -> c#(c(b(x1)))
     c#(b(x1)) -> b#(a(x1))
    TRS:
     b(a(x1)) -> x1
     c(a(x1)) -> a(c(c(b(x1))))
     c(b(x1)) -> b(a(x1))
    graph:
     c#(a(x1)) -> c#(c(b(x1))) -> c#(b(x1)) -> b#(a(x1))
     c#(a(x1)) -> c#(c(b(x1))) -> c#(a(x1)) -> c#(c(b(x1)))
     c#(a(x1)) -> c#(c(b(x1))) -> c#(a(x1)) -> c#(b(x1))
     c#(a(x1)) -> c#(c(b(x1))) -> c#(a(x1)) -> b#(x1)
     c#(a(x1)) -> c#(b(x1)) -> c#(b(x1)) -> b#(a(x1))
     c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> c#(c(b(x1)))
     c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> c#(b(x1))
     c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 8/16
     DPs:
      c#(a(x1)) -> c#(c(b(x1)))
      c#(a(x1)) -> c#(b(x1))
     TRS:
      b(a(x1)) -> x1
      c(a(x1)) -> a(c(c(b(x1))))
      c(b(x1)) -> b(a(x1))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       b(a(x1)) -> x1
       c(a(x1)) -> a(c(c(b(x1))))
       c(b(x1)) -> b(a(x1))
      interpretation:
       [c#](x0) = [-& 0 ]x0 + [1],
       
                 [0 1]     [2]
       [c](x0) = [0 0]x0 + [2],
       
                 [-& 1 ]     [3]
       [a](x0) = [0  0 ]x0 + [2],
       
                 [-1 0 ]     [0]
       [b](x0) = [-1 -&]x0 + [0]
      orientation:
       c#(a(x1)) = [0 0]x1 + [2] >= [-1 0 ]x1 + [2] = c#(c(b(x1)))
       
       c#(a(x1)) = [0 0]x1 + [2] >= [-1 -&]x1 + [1] = c#(b(x1))
       
                  [0  0 ]     [2]           
       b(a(x1)) = [-& 0 ]x1 + [2] >= x1 = x1
       
                  [1 1]     [3]    [1 1]     [3]                 
       c(a(x1)) = [0 1]x1 + [3] >= [0 1]x1 + [3] = a(c(c(b(x1))))
       
                  [0  0 ]     [2]    [0  0 ]     [2]           
       c(b(x1)) = [-1 0 ]x1 + [2] >= [-& 0 ]x1 + [2] = b(a(x1))
      problem:
       DPs:
        c#(a(x1)) -> c#(c(b(x1)))
       TRS:
        b(a(x1)) -> x1
        c(a(x1)) -> a(c(c(b(x1))))
        c(b(x1)) -> b(a(x1))
      Restore Modifier:
       DPs:
        c#(a(x1)) -> c#(c(b(x1)))
       TRS:
        b(a(x1)) -> x1
        c(a(x1)) -> a(c(c(b(x1))))
        c(b(x1)) -> b(a(x1))
       EDG Processor:
        DPs:
         c#(a(x1)) -> c#(c(b(x1)))
        TRS:
         b(a(x1)) -> x1
         c(a(x1)) -> a(c(c(b(x1))))
         c(b(x1)) -> b(a(x1))
        graph:
         c#(a(x1)) -> c#(c(b(x1))) -> c#(a(x1)) -> c#(c(b(x1)))
        Arctic Interpretation Processor:
         dimension: 2
         usable rules:
          b(a(x1)) -> x1
          c(a(x1)) -> a(c(c(b(x1))))
          c(b(x1)) -> b(a(x1))
         interpretation:
          [c#](x0) = [0  -&]x0 + [0],
          
                    [1  -&]     [-4]
          [c](x0) = [-& 0 ]x0 + [-4],
          
                    [1  -&]     [2 ]
          [a](x0) = [-& 0 ]x0 + [-3],
          
                    [-1 -&]     [0 ]
          [b](x0) = [-& 0 ]x0 + [-3]
         orientation:
          c#(a(x1)) = [1  -&]x1 + [2] >= [0  -&]x1 + [1] = c#(c(b(x1)))
          
                          [1 ]           
          b(a(x1)) = x1 + [-3] >= x1 = x1
          
                     [2  -&]     [3 ]    [2  -&]     [3 ]                 
          c(a(x1)) = [-& 0 ]x1 + [-3] >= [-& 0 ]x1 + [-3] = a(c(c(b(x1))))
          
                          [1 ]         [1 ]           
          c(b(x1)) = x1 + [-3] >= x1 + [-3] = b(a(x1))
         problem:
          DPs:
           
          TRS:
           b(a(x1)) -> x1
           c(a(x1)) -> a(c(c(b(x1))))
           c(b(x1)) -> b(a(x1))
         Qed