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))
     KBO Processor:
      argument filtering:
       pi(a) = 0
       pi(b) = [0]
       pi(c) = 0
       pi(b#) = 0
       pi(c#) = 0
      usable rules:
       a(x1) -> x1
       b(a(a(x1))) -> a(b(c(c(x1))))
       c(b(x1)) -> b(a(x1))
      weight function:
       w0 = 1
       w(b) = 1
       w(c#) = w(b#) = w(c) = w(a) = 0
      precedence:
       b > a > c > c# > b#
      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*
            b1(22) -> 23*
            b1(36) -> 37*
            b1(17) -> 18*
            b1(29) -> 30*
            c0(1) -> 1*
            c0(6) -> 7*
            c0(3) -> 1*
            c0(4) -> 6*
            c0(2) -> 1*
            c1(35) -> 36*
            c1(13) -> 14*
            c1(12) -> 13*
            c1(34) -> 35*
            c1(48) -> 49*
            b{#,1}(14) -> 15*
            b0(2) -> 3*
            b0(3) -> 3*
            b0(1) -> 3*
            a1(52) -> 53*
            a1(58) -> 59*
            a1(28) -> 29*
            a1(37) -> 38*
            a1(23) -> 24*
            a1(46) -> 47*
            a1(16) -> 17*
            a0(1) -> 2*
            a0(2) -> 2*
            a0(3) -> 2*
            24 -> 18,13
            47 -> 29*
            17 -> 28*
            46 -> 47*
            30 -> 36,14
            14 -> 22*
            16 -> 34,17
            28 -> 29*
            2 -> 16,3,4
            53 -> 17*
            22 -> 46*
            52 -> 53,17
            36 -> 52*
            58 -> 59,29,13,49
            38 -> 30,14,22
            1 -> 12,2,4
            49 -> 35*
            59 -> 29*
            37 -> 48,38,14
            3 -> 7,1,6,2,4
            18 -> 49,35,13
            15 -> 5*
            29 -> 58,13,49
            23 -> 24,13
          problem:
           DPs:
            
           TRS:
            a(x1) -> x1
            b(a(a(x1))) -> a(b(c(c(x1))))
            c(b(x1)) -> b(a(x1))
          Qed