YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(a(x1))) -> a(b(c(c(x1))))
  c(b(x1)) -> b(a(x1))
  DP Processor:
   DPs:
    b#(a(a(x1))) -> c#(x1)
    b#(a(a(x1))) -> c#(c(x1))
    b#(a(a(x1))) -> b#(c(c(x1)))
    b#(a(a(x1))) -> a#(b(c(c(x1))))
    c#(b(x1)) -> a#(x1)
    c#(b(x1)) -> b#(a(x1))
   TRS:
    a(x1) -> x1
    b(a(a(x1))) -> a(b(c(c(x1))))
    c(b(x1)) -> b(a(x1))
   TDG Processor:
    DPs:
     b#(a(a(x1))) -> c#(x1)
     b#(a(a(x1))) -> c#(c(x1))
     b#(a(a(x1))) -> b#(c(c(x1)))
     b#(a(a(x1))) -> a#(b(c(c(x1))))
     c#(b(x1)) -> a#(x1)
     c#(b(x1)) -> b#(a(x1))
    TRS:
     a(x1) -> x1
     b(a(a(x1))) -> a(b(c(c(x1))))
     c(b(x1)) -> b(a(x1))
    graph:
     c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(c(x1))))
     c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(c(x1)))
     c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(c(x1))
     c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1)
     b#(a(a(x1))) -> c#(c(x1)) -> c#(b(x1)) -> b#(a(x1))
     b#(a(a(x1))) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1)
     b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1))
     b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> a#(x1)
     b#(a(a(x1))) -> b#(c(c(x1))) -> b#(a(a(x1))) -> a#(b(c(c(x1))))
     b#(a(a(x1))) -> b#(c(c(x1))) -> b#(a(a(x1))) -> b#(c(c(x1)))
     b#(a(a(x1))) -> b#(c(c(x1))) -> b#(a(a(x1))) -> c#(c(x1))
     b#(a(a(x1))) -> b#(c(c(x1))) -> b#(a(a(x1))) -> c#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 12/36
     DPs:
      c#(b(x1)) -> b#(a(x1))
      b#(a(a(x1))) -> c#(x1)
      b#(a(a(x1))) -> c#(c(x1))
      b#(a(a(x1))) -> b#(c(c(x1)))
     TRS:
      a(x1) -> x1
      b(a(a(x1))) -> a(b(c(c(x1))))
      c(b(x1)) -> b(a(x1))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       b(a(a(x1))) -> a(b(c(c(x1))))
       c(b(x1)) -> b(a(x1))
      interpretation:
       [c#](x0) = [0 0]x0 + [0],
       
       [b#](x0) = [0 0]x0 + [0],
       
                 [0 0]     [0]
       [c](x0) = [0 0]x0 + [0],
       
                 [1  0 ]     [-&]
       [b](x0) = [-& 1 ]x0 + [1 ],
       
                 [0 0]     [-&]
       [a](x0) = [0 0]x0 + [0 ]
      orientation:
       c#(b(x1)) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(a(x1))
       
       b#(a(a(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c#(x1)
       
       b#(a(a(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c#(c(x1))
       
       b#(a(a(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = b#(c(c(x1)))
       
               [0 0]     [-&]           
       a(x1) = [0 0]x1 + [0 ] >= x1 = x1
       
                     [1 1]     [1]    [1 1]     [1]                 
       b(a(a(x1))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a(b(c(c(x1))))
       
                  [1 1]     [1]    [1 1]     [0]           
       c(b(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = b(a(x1))
      problem:
       DPs:
        b#(a(a(x1))) -> c#(x1)
        b#(a(a(x1))) -> c#(c(x1))
        b#(a(a(x1))) -> b#(c(c(x1)))
       TRS:
        a(x1) -> x1
        b(a(a(x1))) -> a(b(c(c(x1))))
        c(b(x1)) -> b(a(x1))
      Restore Modifier:
       DPs:
        b#(a(a(x1))) -> c#(x1)
        b#(a(a(x1))) -> c#(c(x1))
        b#(a(a(x1))) -> b#(c(c(x1)))
       TRS:
        a(x1) -> x1
        b(a(a(x1))) -> a(b(c(c(x1))))
        c(b(x1)) -> b(a(x1))
       EDG Processor:
        DPs:
         b#(a(a(x1))) -> c#(x1)
         b#(a(a(x1))) -> c#(c(x1))
         b#(a(a(x1))) -> b#(c(c(x1)))
        TRS:
         a(x1) -> x1
         b(a(a(x1))) -> a(b(c(c(x1))))
         c(b(x1)) -> b(a(x1))
        graph:
         b#(a(a(x1))) -> b#(c(c(x1))) -> b#(a(a(x1))) -> c#(x1)
         b#(a(a(x1))) -> b#(c(c(x1))) -> b#(a(a(x1))) -> c#(c(x1))
         b#(a(a(x1))) -> b#(c(c(x1))) -> b#(a(a(x1))) -> b#(c(c(x1)))
        SCC Processor:
         #sccs: 1
         #rules: 1
         #arcs: 3/9
         DPs:
          b#(a(a(x1))) -> b#(c(c(x1)))
         TRS:
          a(x1) -> x1
          b(a(a(x1))) -> a(b(c(c(x1))))
          c(b(x1)) -> b(a(x1))
         Bounds Processor:
          bound: 1
          enrichment: match-dp
          automaton:
           final states: {5}
           transitions:
            b{#,0}(7) -> 5*
            a0(2) -> 2*
            a0(1) -> 2*
            a0(3) -> 2*
            c0(2) -> 1*
            c0(4) -> 6*
            c0(6) -> 7*
            c0(1) -> 1*
            c0(3) -> 1*
            b0(2) -> 3*
            b0(1) -> 3*
            b0(3) -> 3*
            b{#,1}(14) -> 15*
            c1(50) -> 51*
            c1(35) -> 36*
            c1(12) -> 13*
            c1(34) -> 35*
            c1(13) -> 14*
            b1(22) -> 23*
            b1(17) -> 18*
            b1(29) -> 30*
            b1(36) -> 37*
            a1(55) -> 56*
            a1(37) -> 38*
            a1(61) -> 62*
            a1(46) -> 47*
            a1(16) -> 17*
            a1(28) -> 29*
            a1(23) -> 24*
            1 -> 2,4
            2 -> 16,12,3,4
            3 -> 7,6,1,2,4
            14 -> 22*
            15 -> 5*
            16 -> 34,17
            17 -> 28*
            18 -> 51,35,13
            22 -> 46*
            23 -> 24,13
            24 -> 18,13
            28 -> 29*
            29 -> 61,13,51
            30 -> 36,14
            36 -> 55*
            37 -> 50,38,14
            38 -> 30,14,22
            46 -> 47,29
            47 -> 29*
            51 -> 35*
            55 -> 56,17,28
            56 -> 17*
            61 -> 62,29,13,51
            62 -> 29*
          problem:
           DPs:
            
           TRS:
            a(x1) -> x1
            b(a(a(x1))) -> a(b(c(c(x1))))
            c(b(x1)) -> b(a(x1))
          Qed