YES

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

Proof:
 String Reversal Processor:
  b(a(x1)) -> x1
  c(b(x1)) -> a(a(x1))
  a(c(x1)) -> c(c(b(b(x1))))
  DP Processor:
   DPs:
    c#(b(x1)) -> a#(x1)
    c#(b(x1)) -> a#(a(x1))
    a#(c(x1)) -> b#(x1)
    a#(c(x1)) -> b#(b(x1))
    a#(c(x1)) -> c#(b(b(x1)))
    a#(c(x1)) -> c#(c(b(b(x1))))
   TRS:
    b(a(x1)) -> x1
    c(b(x1)) -> a(a(x1))
    a(c(x1)) -> c(c(b(b(x1))))
   TDG Processor:
    DPs:
     c#(b(x1)) -> a#(x1)
     c#(b(x1)) -> a#(a(x1))
     a#(c(x1)) -> b#(x1)
     a#(c(x1)) -> b#(b(x1))
     a#(c(x1)) -> c#(b(b(x1)))
     a#(c(x1)) -> c#(c(b(b(x1))))
    TRS:
     b(a(x1)) -> x1
     c(b(x1)) -> a(a(x1))
     a(c(x1)) -> c(c(b(b(x1))))
    graph:
     a#(c(x1)) -> c#(c(b(b(x1)))) -> c#(b(x1)) -> a#(a(x1))
     a#(c(x1)) -> c#(c(b(b(x1)))) -> c#(b(x1)) -> a#(x1)
     a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(a(x1))
     a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(x1)
     c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(c(b(b(x1))))
     c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(b(b(x1)))
     c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(b(x1))
     c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> b#(x1)
     c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(c(b(b(x1))))
     c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(b(b(x1)))
     c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(b(x1))
     c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 12/36
     DPs:
      a#(c(x1)) -> c#(c(b(b(x1))))
      c#(b(x1)) -> a#(x1)
      a#(c(x1)) -> c#(b(b(x1)))
      c#(b(x1)) -> a#(a(x1))
     TRS:
      b(a(x1)) -> x1
      c(b(x1)) -> a(a(x1))
      a(c(x1)) -> c(c(b(b(x1))))
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [a#](x0) = [0 0]x0 + [0],
       
       [c#](x0) = [0  -&]x0 + [1],
       
                 [-& -&]     [0]
       [c](x0) = [0  0 ]x0 + [2],
       
                 [-& -&]     [0]
       [a](x0) = [0  0 ]x0 + [0],
       
                 [0 0]     [0]
       [b](x0) = [0 0]x0 + [1]
      orientation:
       a#(c(x1)) = [0 0]x1 + [2] >= [1] = c#(c(b(b(x1))))
       
       c#(b(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [0] = a#(x1)
       
       a#(c(x1)) = [0 0]x1 + [2] >= [0 0]x1 + [1] = c#(b(b(x1)))
       
       c#(b(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [0] = a#(a(x1))
       
                  [0 0]     [0]           
       b(a(x1)) = [0 0]x1 + [1] >= x1 = x1
       
                  [-& -&]     [0]    [-& -&]     [0]           
       c(b(x1)) = [0  0 ]x1 + [2] >= [0  0 ]x1 + [0] = a(a(x1))
       
                  [-& -&]     [0]    [-& -&]     [0]                 
       a(c(x1)) = [0  0 ]x1 + [2] >= [0  0 ]x1 + [2] = c(c(b(b(x1))))
      problem:
       DPs:
        c#(b(x1)) -> a#(x1)
        a#(c(x1)) -> c#(b(b(x1)))
        c#(b(x1)) -> a#(a(x1))
       TRS:
        b(a(x1)) -> x1
        c(b(x1)) -> a(a(x1))
        a(c(x1)) -> c(c(b(b(x1))))
      EDG Processor:
       DPs:
        c#(b(x1)) -> a#(x1)
        a#(c(x1)) -> c#(b(b(x1)))
        c#(b(x1)) -> a#(a(x1))
       TRS:
        b(a(x1)) -> x1
        c(b(x1)) -> a(a(x1))
        a(c(x1)) -> c(c(b(b(x1))))
       graph:
        a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(x1)
        a#(c(x1)) -> c#(b(b(x1))) -> c#(b(x1)) -> a#(a(x1))
        c#(b(x1)) -> a#(a(x1)) -> a#(c(x1)) -> c#(b(b(x1)))
        c#(b(x1)) -> a#(x1) -> a#(c(x1)) -> c#(b(b(x1)))
       Arctic Interpretation Processor:
        dimension: 2
        interpretation:
         [a#](x0) = [0 0]x0,
         
         [c#](x0) = [1 0]x0 + [0],
         
                   [1 0]     [0]
         [c](x0) = [2 1]x0 + [3],
         
                   [0 0]     [0]
         [a](x0) = [0 1]x0 + [0],
         
                   [-& 0 ]     [1]
         [b](x0) = [0  -&]x0 + [0]
        orientation:
         c#(b(x1)) = [0 1]x1 + [2] >= [0 0]x1 = a#(x1)
         
         a#(c(x1)) = [2 1]x1 + [3] >= [1 0]x1 + [2] = c#(b(b(x1)))
         
         c#(b(x1)) = [0 1]x1 + [2] >= [0 1]x1 + [0] = a#(a(x1))
         
                    [0 1]     [1]           
         b(a(x1)) = [0 0]x1 + [0] >= x1 = x1
         
                    [0 1]     [2]    [0 1]     [0]           
         c(b(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [1] = a(a(x1))
         
                    [2 1]     [3]    [2 1]     [3]                 
         a(c(x1)) = [3 2]x1 + [4] >= [3 2]x1 + [4] = c(c(b(b(x1))))
        problem:
         DPs:
          c#(b(x1)) -> a#(x1)
          c#(b(x1)) -> a#(a(x1))
         TRS:
          b(a(x1)) -> x1
          c(b(x1)) -> a(a(x1))
          a(c(x1)) -> c(c(b(b(x1))))
        EDG Processor:
         DPs:
          c#(b(x1)) -> a#(x1)
          c#(b(x1)) -> a#(a(x1))
         TRS:
          b(a(x1)) -> x1
          c(b(x1)) -> a(a(x1))
          a(c(x1)) -> c(c(b(b(x1))))
         graph:
          
         Qed