YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  a(a(x1)) -> b(c(a(b(x1))))
  b(x1) -> c(x1)
  c(b(x1)) -> a(x1)
  DP Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> a#(b(x1))
    a#(a(x1)) -> c#(a(b(x1)))
    a#(a(x1)) -> b#(c(a(b(x1))))
    b#(x1) -> c#(x1)
    c#(b(x1)) -> a#(x1)
   TRS:
    a(x1) -> x1
    a(a(x1)) -> b(c(a(b(x1))))
    b(x1) -> c(x1)
    c(b(x1)) -> a(x1)
   TDG Processor:
    DPs:
     a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> a#(b(x1))
     a#(a(x1)) -> c#(a(b(x1)))
     a#(a(x1)) -> b#(c(a(b(x1))))
     b#(x1) -> c#(x1)
     c#(b(x1)) -> a#(x1)
    TRS:
     a(x1) -> x1
     a(a(x1)) -> b(c(a(b(x1))))
     b(x1) -> c(x1)
     c(b(x1)) -> a(x1)
    graph:
     c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(c(a(b(x1))))
     c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(a(b(x1)))
     c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(x1))
     c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
     b#(x1) -> c#(x1) -> c#(b(x1)) -> a#(x1)
     a#(a(x1)) -> c#(a(b(x1))) -> c#(b(x1)) -> a#(x1)
     a#(a(x1)) -> b#(c(a(b(x1)))) -> b#(x1) -> c#(x1)
     a#(a(x1)) -> b#(x1) -> b#(x1) -> c#(x1)
     a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(c(a(b(x1))))
     a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> c#(a(b(x1)))
     a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> a#(b(x1))
     a#(a(x1)) -> a#(b(x1)) -> a#(a(x1)) -> b#(x1)
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
      [c#](x0) = [2 1]x0 + [0],
      
      [b#](x0) = [2 2]x0 + [0],
      
      [a#](x0) = [1 2]x0 + [0],
      
                [0  -&]     [0 ]
      [c](x0) = [0  -&]x0 + [-&],
      
                [1 1]     [0 ]
      [b](x0) = [0 0]x0 + [-&],
      
                [0 1]     [-&]
      [a](x0) = [1 1]x0 + [0 ]
     orientation:
      a#(a(x1)) = [3 3]x1 + [2] >= [2 2]x1 + [0] = b#(x1)
      
      a#(a(x1)) = [3 3]x1 + [2] >= [2 2]x1 + [1] = a#(b(x1))
      
      a#(a(x1)) = [3 3]x1 + [2] >= [3 3]x1 + [2] = c#(a(b(x1)))
      
      a#(a(x1)) = [3 3]x1 + [2] >= [3 3]x1 + [2] = b#(c(a(b(x1))))
      
      b#(x1) = [2 2]x1 + [0] >= [2 1]x1 + [0] = c#(x1)
      
      c#(b(x1)) = [3 3]x1 + [2] >= [1 2]x1 + [0] = a#(x1)
      
              [0 1]     [-&]           
      a(x1) = [1 1]x1 + [0 ] >= x1 = x1
      
                 [2 2]     [1]    [2 2]     [1]                 
      a(a(x1)) = [2 2]x1 + [1] >= [1 1]x1 + [0] = b(c(a(b(x1))))
      
              [1 1]     [0 ]    [0  -&]     [0 ]        
      b(x1) = [0 0]x1 + [-&] >= [0  -&]x1 + [-&] = c(x1)
      
                 [1 1]     [0]    [0 1]     [-&]        
      c(b(x1)) = [1 1]x1 + [0] >= [1 1]x1 + [0 ] = a(x1)
     problem:
      DPs:
       a#(a(x1)) -> c#(a(b(x1)))
       a#(a(x1)) -> b#(c(a(b(x1))))
       b#(x1) -> c#(x1)
      TRS:
       a(x1) -> x1
       a(a(x1)) -> b(c(a(b(x1))))
       b(x1) -> c(x1)
       c(b(x1)) -> a(x1)
     EDG Processor:
      DPs:
       a#(a(x1)) -> c#(a(b(x1)))
       a#(a(x1)) -> b#(c(a(b(x1))))
       b#(x1) -> c#(x1)
      TRS:
       a(x1) -> x1
       a(a(x1)) -> b(c(a(b(x1))))
       b(x1) -> c(x1)
       c(b(x1)) -> a(x1)
      graph:
       a#(a(x1)) -> b#(c(a(b(x1)))) -> b#(x1) -> c#(x1)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 1/9