YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> c(b(x1))
  b(x1) -> x1
  c(c(x1)) -> a(b(c(a(x1))))
  DP Processor:
   DPs:
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> c#(b(x1))
    c#(c(x1)) -> a#(x1)
    c#(c(x1)) -> c#(a(x1))
    c#(c(x1)) -> b#(c(a(x1)))
    c#(c(x1)) -> a#(b(c(a(x1))))
   TRS:
    a(x1) -> x1
    b(a(x1)) -> c(b(x1))
    b(x1) -> x1
    c(c(x1)) -> a(b(c(a(x1))))
   TDG Processor:
    DPs:
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> c#(b(x1))
     c#(c(x1)) -> a#(x1)
     c#(c(x1)) -> c#(a(x1))
     c#(c(x1)) -> b#(c(a(x1)))
     c#(c(x1)) -> a#(b(c(a(x1))))
    TRS:
     a(x1) -> x1
     b(a(x1)) -> c(b(x1))
     b(x1) -> x1
     c(c(x1)) -> a(b(c(a(x1))))
    graph:
     c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(b(c(a(x1))))
     c#(c(x1)) -> c#(a(x1)) -> c#(c(x1)) -> b#(c(a(x1)))
     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)) -> b#(c(a(x1))) -> b#(a(x1)) -> c#(b(x1))
     c#(c(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(b(c(a(x1))))
     b#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(c(a(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)) -> 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#(c(x1)) -> b#(c(a(x1)))
      b#(a(x1)) -> b#(x1)
      b#(a(x1)) -> c#(b(x1))
     TRS:
      a(x1) -> x1
      b(a(x1)) -> c(b(x1))
      b(x1) -> x1
      c(c(x1)) -> a(b(c(a(x1))))
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [c#](x0) = [-& 0 ]x0 + [0],
       
       [b#](x0) = [0  -&]x0 + [0],
       
                 [-& 0 ]     [1]
       [c](x0) = [-& 2 ]x0 + [3],
       
                 [0  -&]     [0]
       [b](x0) = [2  0 ]x0 + [0],
       
                 [2  0 ]     [1]
       [a](x0) = [-& 0 ]x0 + [1]
      orientation:
       c#(c(x1)) = [-& 2 ]x1 + [3] >= [-& 0 ]x1 + [1] = c#(a(x1))
       
       c#(c(x1)) = [-& 2 ]x1 + [3] >= [-& 0 ]x1 + [1] = b#(c(a(x1)))
       
       b#(a(x1)) = [2 0]x1 + [1] >= [0  -&]x1 + [0] = b#(x1)
       
       b#(a(x1)) = [2 0]x1 + [1] >= [2 0]x1 + [0] = c#(b(x1))
       
               [2  0 ]     [1]           
       a(x1) = [-& 0 ]x1 + [1] >= x1 = x1
       
                  [2 0]     [1]    [2 0]     [1]           
       b(a(x1)) = [4 2]x1 + [3] >= [4 2]x1 + [3] = c(b(x1))
       
               [0  -&]     [0]           
       b(x1) = [2  0 ]x1 + [0] >= x1 = x1
       
                  [-& 2 ]     [3]    [-& 2 ]     [3]                 
       c(c(x1)) = [-& 4 ]x1 + [5] >= [-& 2 ]x1 + [3] = a(b(c(a(x1))))
      problem:
       DPs:
        b#(a(x1)) -> c#(b(x1))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> c(b(x1))
        b(x1) -> x1
        c(c(x1)) -> a(b(c(a(x1))))
      EDG Processor:
       DPs:
        b#(a(x1)) -> c#(b(x1))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> c(b(x1))
        b(x1) -> x1
        c(c(x1)) -> a(b(c(a(x1))))
       graph:
        
       Qed