YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(b(a(x1))) -> c(b(b(b(x1))))
  b(c(x1)) -> a(a(x1))
  DP Processor:
   DPs:
    b#(b(a(x1))) -> b#(x1)
    b#(b(a(x1))) -> b#(b(x1))
    b#(b(a(x1))) -> b#(b(b(x1)))
    b#(c(x1)) -> a#(x1)
    b#(c(x1)) -> a#(a(x1))
   TRS:
    a(x1) -> x1
    b(b(a(x1))) -> c(b(b(b(x1))))
    b(c(x1)) -> a(a(x1))
   TDG Processor:
    DPs:
     b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(b(b(x1)))
     b#(c(x1)) -> a#(x1)
     b#(c(x1)) -> a#(a(x1))
    TRS:
     a(x1) -> x1
     b(b(a(x1))) -> c(b(b(b(x1))))
     b(c(x1)) -> a(a(x1))
    graph:
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(c(x1)) -> a#(a(x1))
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(c(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> b#(b(b(x1)))
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(b(x1)) -> b#(c(x1)) -> a#(a(x1))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(c(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(b(x1)))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(x1) -> b#(c(x1)) -> a#(a(x1))
     b#(b(a(x1))) -> b#(x1) -> b#(c(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(b(b(x1)))
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 15/25
     DPs:
      b#(b(a(x1))) -> b#(b(b(x1)))
      b#(b(a(x1))) -> b#(x1)
      b#(b(a(x1))) -> b#(b(x1))
     TRS:
      a(x1) -> x1
      b(b(a(x1))) -> c(b(b(b(x1))))
      b(c(x1)) -> a(a(x1))
     Arctic Interpretation Processor:
      dimension: 3
      usable rules:
       a(x1) -> x1
       b(b(a(x1))) -> c(b(b(b(x1))))
       b(c(x1)) -> a(a(x1))
      interpretation:
       [b#](x0) = [-& 0  -&]x0 + [0],
       
                 [-& 0  -&]     [0 ]
       [b](x0) = [-& -& 0 ]x0 + [-&]
                 [0  -& -&]     [0 ],
       
                 [0  -& -&]     [-&]
       [a](x0) = [0  0  -&]x0 + [-&]
                 [1  0  0 ]     [1 ],
       
                 [1  0  0 ]     [1]
       [c](x0) = [0  -& -&]x0 + [0]
                 [0  0  -&]     [0]
      orientation:
       b#(b(a(x1))) = [1 0 0]x1 + [1] >= [0  -& -&]x1 + [0] = b#(b(b(x1)))
       
       b#(b(a(x1))) = [1 0 0]x1 + [1] >= [-& 0  -&]x1 + [0] = b#(x1)
       
       b#(b(a(x1))) = [1 0 0]x1 + [1] >= [-& -& 0 ]x1 + [0] = b#(b(x1))
       
               [0  -& -&]     [-&]           
       a(x1) = [0  0  -&]x1 + [-&] >= x1 = x1
               [1  0  0 ]     [1 ]           
       
                     [1  0  0 ]     [1]    [1  0  0 ]     [1]                 
       b(b(a(x1))) = [0  -& -&]x1 + [0] >= [0  -& -&]x1 + [0] = c(b(b(b(x1))))
                     [0  0  -&]     [0]    [0  0  -&]     [0]                 
       
                  [0  -& -&]     [0]    [0  -& -&]     [-&]           
       b(c(x1)) = [0  0  -&]x1 + [0] >= [0  0  -&]x1 + [-&] = a(a(x1))
                  [1  0  0 ]     [1]    [1  0  0 ]     [1 ]           
      problem:
       DPs:
        b#(b(a(x1))) -> b#(x1)
        b#(b(a(x1))) -> b#(b(x1))
       TRS:
        a(x1) -> x1
        b(b(a(x1))) -> c(b(b(b(x1))))
        b(c(x1)) -> a(a(x1))
      Restore Modifier:
       DPs:
        b#(b(a(x1))) -> b#(x1)
        b#(b(a(x1))) -> b#(b(x1))
       TRS:
        a(x1) -> x1
        b(b(a(x1))) -> c(b(b(b(x1))))
        b(c(x1)) -> a(a(x1))
       EDG Processor:
        DPs:
         b#(b(a(x1))) -> b#(x1)
         b#(b(a(x1))) -> b#(b(x1))
        TRS:
         a(x1) -> x1
         b(b(a(x1))) -> c(b(b(b(x1))))
         b(c(x1)) -> a(a(x1))
        graph:
         b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(x1)
         b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1))
         b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(x1)
         b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(b(x1))
        Arctic Interpretation Processor:
         dimension: 1
         usable rules:
          a(x1) -> x1
          b(b(a(x1))) -> c(b(b(b(x1))))
          b(c(x1)) -> a(a(x1))
         interpretation:
          [b#](x0) = x0,
          
          [b](x0) = 1x0,
          
          [a](x0) = x0 + 0,
          
          [c](x0) = -1x0 + 0
         orientation:
          b#(b(a(x1))) = 1x1 + 1 >= x1 = b#(x1)
          
          b#(b(a(x1))) = 1x1 + 1 >= 1x1 = b#(b(x1))
          
          a(x1) = x1 + 0 >= x1 = x1
          
          b(b(a(x1))) = 2x1 + 2 >= 2x1 + 0 = c(b(b(b(x1))))
          
          b(c(x1)) = x1 + 1 >= x1 + 0 = a(a(x1))
         problem:
          DPs:
           b#(b(a(x1))) -> b#(b(x1))
          TRS:
           a(x1) -> x1
           b(b(a(x1))) -> c(b(b(b(x1))))
           b(c(x1)) -> a(a(x1))
         Restore Modifier:
          DPs:
           b#(b(a(x1))) -> b#(b(x1))
          TRS:
           a(x1) -> x1
           b(b(a(x1))) -> c(b(b(b(x1))))
           b(c(x1)) -> a(a(x1))
          EDG Processor:
           DPs:
            b#(b(a(x1))) -> b#(b(x1))
           TRS:
            a(x1) -> x1
            b(b(a(x1))) -> c(b(b(b(x1))))
            b(c(x1)) -> a(a(x1))
           graph:
            b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1))
           Bounds Processor:
            bound: 0
            enrichment: match-dp
            automaton:
             final states: {1}
             transitions:
              f50() -> 2*
              b0(5) -> 6*
              b0(4) -> 5*
              b0(2) -> 3*
              b{#,0}(3) -> 1*
              a0(16) -> 17*
              a0(15) -> 16*
              a0(18) -> 19*
              a0(19) -> 20*
              c0(6) -> 7*
              19 -> 20,4
              17 -> 15,5
              7 -> 6,15,16,5,3
              16 -> 6,17
              2 -> 18*
              6 -> 15*
              20 -> 17,5,3
              3 -> 4*
              18 -> 19*
              15 -> 16*
            problem:
             DPs:
              
             TRS:
              a(x1) -> x1
              b(b(a(x1))) -> c(b(b(b(x1))))
              b(c(x1)) -> a(a(x1))
            Qed