YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  a(a(x1)) -> a(c(b(a(x1))))
  b(c(x1)) -> a(b(a(x1)))
  DP Processor:
   DPs:
    a#(a(x1)) -> b#(a(x1))
    a#(a(x1)) -> a#(c(b(a(x1))))
    b#(c(x1)) -> a#(x1)
    b#(c(x1)) -> b#(a(x1))
    b#(c(x1)) -> a#(b(a(x1)))
   TRS:
    a(x1) -> x1
    a(a(x1)) -> a(c(b(a(x1))))
    b(c(x1)) -> a(b(a(x1)))
   TDG Processor:
    DPs:
     a#(a(x1)) -> b#(a(x1))
     a#(a(x1)) -> a#(c(b(a(x1))))
     b#(c(x1)) -> a#(x1)
     b#(c(x1)) -> b#(a(x1))
     b#(c(x1)) -> a#(b(a(x1)))
    TRS:
     a(x1) -> x1
     a(a(x1)) -> a(c(b(a(x1))))
     b(c(x1)) -> a(b(a(x1)))
    graph:
     b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(a(x1)))
     b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(a(x1))
     b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1)
     b#(c(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(c(b(a(x1))))
     b#(c(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1))
     b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(b(a(x1))))
     b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
     a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(a(x1)))
     a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(a(x1))
     a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1)
     a#(a(x1)) -> a#(c(b(a(x1)))) -> a#(a(x1)) -> a#(c(b(a(x1))))
     a#(a(x1)) -> a#(c(b(a(x1)))) -> a#(a(x1)) -> b#(a(x1))
    EDG Processor:
     DPs:
      a#(a(x1)) -> b#(a(x1))
      a#(a(x1)) -> a#(c(b(a(x1))))
      b#(c(x1)) -> a#(x1)
      b#(c(x1)) -> b#(a(x1))
      b#(c(x1)) -> a#(b(a(x1)))
     TRS:
      a(x1) -> x1
      a(a(x1)) -> a(c(b(a(x1))))
      b(c(x1)) -> a(b(a(x1)))
     graph:
      b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1)
      b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(a(x1))
      b#(c(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(a(x1)))
      b#(c(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1))
      b#(c(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(c(b(a(x1))))
      b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
      b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(b(a(x1))))
      a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1)
      a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(a(x1))
      a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(b(a(x1)))
     SCC Processor:
      #sccs: 1
      #rules: 4
      #arcs: 10/25
      DPs:
       b#(c(x1)) -> b#(a(x1))
       b#(c(x1)) -> a#(b(a(x1)))
       a#(a(x1)) -> b#(a(x1))
       b#(c(x1)) -> a#(x1)
      TRS:
       a(x1) -> x1
       a(a(x1)) -> a(c(b(a(x1))))
       b(c(x1)) -> a(b(a(x1)))
      Arctic Interpretation Processor:
       dimension: 2
       usable rules:
        a(x1) -> x1
        a(a(x1)) -> a(c(b(a(x1))))
        b(c(x1)) -> a(b(a(x1)))
       interpretation:
        [b#](x0) = [-& 0 ]x0 + [0],
        
        [a#](x0) = [0 1]x0 + [0],
        
                  [-& 0 ]     [0]
        [b](x0) = [-& 0 ]x0 + [1],
        
                  [0 0]     [0]
        [c](x0) = [1 1]x0 + [2],
        
                  [1 1]     [2]
        [a](x0) = [0 0]x0 + [0]
       orientation:
        b#(c(x1)) = [1 1]x1 + [2] >= [0 0]x1 + [0] = b#(a(x1))
        
        b#(c(x1)) = [1 1]x1 + [2] >= [1 1]x1 + [2] = a#(b(a(x1)))
        
        a#(a(x1)) = [1 1]x1 + [2] >= [0 0]x1 + [0] = b#(a(x1))
        
        b#(c(x1)) = [1 1]x1 + [2] >= [0 1]x1 + [0] = a#(x1)
        
                [1 1]     [2]           
        a(x1) = [0 0]x1 + [0] >= x1 = x1
        
                   [2 2]     [3]    [2 2]     [3]                 
        a(a(x1)) = [1 1]x1 + [2] >= [1 1]x1 + [2] = a(c(b(a(x1))))
        
                   [1 1]     [2]    [1 1]     [2]              
        b(c(x1)) = [1 1]x1 + [2] >= [0 0]x1 + [1] = a(b(a(x1)))
       problem:
        DPs:
         b#(c(x1)) -> a#(b(a(x1)))
         b#(c(x1)) -> a#(x1)
        TRS:
         a(x1) -> x1
         a(a(x1)) -> a(c(b(a(x1))))
         b(c(x1)) -> a(b(a(x1)))
       Restore Modifier:
        DPs:
         b#(c(x1)) -> a#(b(a(x1)))
         b#(c(x1)) -> a#(x1)
        TRS:
         a(x1) -> x1
         a(a(x1)) -> a(c(b(a(x1))))
         b(c(x1)) -> a(b(a(x1)))
        EDG Processor:
         DPs:
          b#(c(x1)) -> a#(b(a(x1)))
          b#(c(x1)) -> a#(x1)
         TRS:
          a(x1) -> x1
          a(a(x1)) -> a(c(b(a(x1))))
          b(c(x1)) -> a(b(a(x1)))
         graph:
          
         Qed