YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  a(x1) -> b(b(x1))
  b(a(x1)) -> c(a(c(a(x1))))
  c(c(x1)) -> x1
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(x1) -> b#(b(x1))
    b#(a(x1)) -> c#(a(x1))
    b#(a(x1)) -> a#(c(a(x1)))
    b#(a(x1)) -> c#(a(c(a(x1))))
   TRS:
    a(x1) -> x1
    a(x1) -> b(b(x1))
    b(a(x1)) -> c(a(c(a(x1))))
    c(c(x1)) -> x1
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1))
     b#(a(x1)) -> c#(a(x1))
     b#(a(x1)) -> a#(c(a(x1)))
     b#(a(x1)) -> c#(a(c(a(x1))))
    TRS:
     a(x1) -> x1
     a(x1) -> b(b(x1))
     b(a(x1)) -> c(a(c(a(x1))))
     c(c(x1)) -> x1
    graph:
     b#(a(x1)) -> a#(c(a(x1))) -> a#(x1) -> b#(b(x1))
     b#(a(x1)) -> a#(c(a(x1))) -> a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(c(a(x1))))
     a#(x1) -> b#(b(x1)) -> b#(a(x1)) -> a#(c(a(x1)))
     a#(x1) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(x1))
     a#(x1) -> b#(x1) -> b#(a(x1)) -> c#(a(c(a(x1))))
     a#(x1) -> b#(x1) -> b#(a(x1)) -> a#(c(a(x1)))
     a#(x1) -> b#(x1) -> b#(a(x1)) -> c#(a(x1))
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 8/25
     DPs:
      b#(a(x1)) -> a#(c(a(x1)))
      a#(x1) -> b#(x1)
      a#(x1) -> b#(b(x1))
     TRS:
      a(x1) -> x1
      a(x1) -> b(b(x1))
      b(a(x1)) -> c(a(c(a(x1))))
      c(c(x1)) -> x1
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       a(x1) -> b(b(x1))
       b(a(x1)) -> c(a(c(a(x1))))
       c(c(x1)) -> x1
      interpretation:
       [b#](x0) = [-& 0 ]x0 + [0],
       
                 [0  1 ]  
       [b](x0) = [-& 0 ]x0,
       
       [a#](x0) = [-& 0 ]x0 + [0],
       
                 [0 1]     [-&]
       [a](x0) = [1 2]x0 + [2 ],
       
                 [0  0 ]     [0 ]
       [c](x0) = [0  -&]x0 + [-&]
      orientation:
       b#(a(x1)) = [1 2]x1 + [2] >= [0 1]x1 + [0] = a#(c(a(x1)))
       
       a#(x1) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = b#(x1)
       
       a#(x1) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = b#(b(x1))
       
               [0 1]     [-&]           
       a(x1) = [1 2]x1 + [2 ] >= x1 = x1
       
               [0 1]     [-&]    [0  1 ]             
       a(x1) = [1 2]x1 + [2 ] >= [-& 0 ]x1 = b(b(x1))
       
                  [2 3]     [3]    [2 3]     [3]                 
       b(a(x1)) = [1 2]x1 + [2] >= [1 2]x1 + [2] = c(a(c(a(x1))))
       
                  [0 0]     [0]           
       c(c(x1)) = [0 0]x1 + [0] >= x1 = x1
      problem:
       DPs:
        a#(x1) -> b#(x1)
        a#(x1) -> b#(b(x1))
       TRS:
        a(x1) -> x1
        a(x1) -> b(b(x1))
        b(a(x1)) -> c(a(c(a(x1))))
        c(c(x1)) -> x1
      Restore Modifier:
       DPs:
        a#(x1) -> b#(x1)
        a#(x1) -> b#(b(x1))
       TRS:
        a(x1) -> x1
        a(x1) -> b(b(x1))
        b(a(x1)) -> c(a(c(a(x1))))
        c(c(x1)) -> x1
       EDG Processor:
        DPs:
         a#(x1) -> b#(x1)
         a#(x1) -> b#(b(x1))
        TRS:
         a(x1) -> x1
         a(x1) -> b(b(x1))
         b(a(x1)) -> c(a(c(a(x1))))
         c(c(x1)) -> x1
        graph:
         
        SCC Processor:
         #sccs: 0
         #rules: 0
         #arcs: 0/4