YES

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

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