YES

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

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