YES

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

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