YES

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

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