YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(b(a(x1))) -> c(b(b(b(x1))))
  c(b(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#(b(a(x1))) -> c#(b(b(b(x1))))
    c#(b(x1)) -> a#(x1)
    c#(b(x1)) -> a#(a(x1))
   TRS:
    a(x1) -> x1
    b(b(a(x1))) -> c(b(b(b(x1))))
    c(b(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#(b(a(x1))) -> c#(b(b(b(x1))))
     c#(b(x1)) -> a#(x1)
     c#(b(x1)) -> a#(a(x1))
    TRS:
     a(x1) -> x1
     b(b(a(x1))) -> c(b(b(b(x1))))
     c(b(x1)) -> a(a(x1))
    graph:
     b#(b(a(x1))) -> c#(b(b(b(x1)))) -> c#(b(x1)) -> a#(a(x1))
     b#(b(a(x1))) -> c#(b(b(b(x1)))) -> c#(b(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> c#(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(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#(b(a(x1))) -> c#(b(b(b(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#(b(a(x1))) -> c#(b(b(b(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: 14/36
     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))))
      c(b(x1)) -> a(a(x1))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       b(b(a(x1))) -> c(b(b(b(x1))))
       c(b(x1)) -> a(a(x1))
      interpretation:
       [b#](x0) = [0 0]x0,
       
                 [0 0]     [-&]
       [b](x0) = [1 0]x0 + [0 ],
       
                 [0 0]     [-&]
       [a](x0) = [0 0]x0 + [0 ],
       
                 [0  -&]     [0]
       [c](x0) = [0  -&]x0 + [0]
      orientation:
       b#(b(a(x1))) = [1 1]x1 + [0] >= [1 1]x1 + [0] = b#(b(b(x1)))
       
       b#(b(a(x1))) = [1 1]x1 + [0] >= [0 0]x1 = b#(x1)
       
       b#(b(a(x1))) = [1 1]x1 + [0] >= [1 0]x1 + [0] = b#(b(x1))
       
               [0 0]     [-&]           
       a(x1) = [0 0]x1 + [0 ] >= x1 = x1
       
                     [1 1]     [0]    [1 1]     [0]                 
       b(b(a(x1))) = [1 1]x1 + [1] >= [1 1]x1 + [0] = c(b(b(b(x1))))
       
                  [0 0]     [0]    [0 0]     [0]           
       c(b(x1)) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(a(x1))
      problem:
       DPs:
        b#(b(a(x1))) -> b#(b(b(x1)))
        b#(b(a(x1))) -> b#(b(x1))
       TRS:
        a(x1) -> x1
        b(b(a(x1))) -> c(b(b(b(x1))))
        c(b(x1)) -> a(a(x1))
      Restore Modifier:
       DPs:
        b#(b(a(x1))) -> b#(b(b(x1)))
        b#(b(a(x1))) -> b#(b(x1))
       TRS:
        a(x1) -> x1
        b(b(a(x1))) -> c(b(b(b(x1))))
        c(b(x1)) -> a(a(x1))
       EDG Processor:
        DPs:
         b#(b(a(x1))) -> b#(b(b(x1)))
         b#(b(a(x1))) -> b#(b(x1))
        TRS:
         a(x1) -> x1
         b(b(a(x1))) -> c(b(b(b(x1))))
         c(b(x1)) -> a(a(x1))
        graph:
         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#(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#(b(b(x1)))
        Arctic Interpretation Processor:
         dimension: 2
         usable rules:
          a(x1) -> x1
          b(b(a(x1))) -> c(b(b(b(x1))))
          c(b(x1)) -> a(a(x1))
         interpretation:
          [b#](x0) = [1 0]x0 + [0],
          
                    [-& 0 ]     [0]
          [b](x0) = [0  -&]x0 + [1],
          
                    [0  -&]     [0]
          [a](x0) = [2  0 ]x0 + [3],
          
                    [-& 0 ]     [0]
          [c](x0) = [0  2 ]x0 + [0]
         orientation:
          b#(b(a(x1))) = [3 1]x1 + [4] >= [1 0]x1 + [2] = b#(b(b(x1)))
          
          b#(b(a(x1))) = [3 1]x1 + [4] >= [0 1]x1 + [1] = b#(b(x1))
          
                  [0  -&]     [0]           
          a(x1) = [2  0 ]x1 + [3] >= x1 = x1
          
                        [0  -&]     [1]    [0  -&]     [1]                 
          b(b(a(x1))) = [2  0 ]x1 + [3] >= [2  0 ]x1 + [3] = c(b(b(b(x1))))
          
                     [0  -&]     [1]    [0  -&]     [0]           
          c(b(x1)) = [2  0 ]x1 + [3] >= [2  0 ]x1 + [3] = 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))))
           c(b(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))))
           c(b(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))))
            c(b(x1)) -> a(a(x1))
           graph:
            b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1))
           Matrix Interpretation Processor: dim=1
            
            usable rules:
             a(x1) -> x1
             b(b(a(x1))) -> c(b(b(b(x1))))
             c(b(x1)) -> a(a(x1))
            interpretation:
             [b#](x0) = x0,
             
             [b](x0) = 2x0,
             
             [a](x0) = x0 + 1/2,
             
             [c](x0) = 1/2x0 + 2
            orientation:
             b#(b(a(x1))) = 2x1 + 1 >= 2x1 = b#(b(x1))
             
             a(x1) = x1 + 1/2 >= x1 = x1
             
             b(b(a(x1))) = 4x1 + 2 >= 4x1 + 2 = c(b(b(b(x1))))
             
             c(b(x1)) = x1 + 2 >= x1 + 1 = a(a(x1))
            problem:
             DPs:
              
             TRS:
              a(x1) -> x1
              b(b(a(x1))) -> c(b(b(b(x1))))
              c(b(x1)) -> a(a(x1))
            Qed