YES

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

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