YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(a(x1))) -> c(a(c(c(x1))))
  c(c(x1)) -> a(b(x1))
  DP Processor:
   DPs:
    b#(a(a(x1))) -> c#(x1)
    b#(a(a(x1))) -> c#(c(x1))
    b#(a(a(x1))) -> a#(c(c(x1)))
    b#(a(a(x1))) -> c#(a(c(c(x1))))
    c#(c(x1)) -> b#(x1)
    c#(c(x1)) -> a#(b(x1))
   TRS:
    a(x1) -> x1
    b(a(a(x1))) -> c(a(c(c(x1))))
    c(c(x1)) -> a(b(x1))
   TDG Processor:
    DPs:
     b#(a(a(x1))) -> c#(x1)
     b#(a(a(x1))) -> c#(c(x1))
     b#(a(a(x1))) -> a#(c(c(x1)))
     b#(a(a(x1))) -> c#(a(c(c(x1))))
     c#(c(x1)) -> b#(x1)
     c#(c(x1)) -> a#(b(x1))
    TRS:
     a(x1) -> x1
     b(a(a(x1))) -> c(a(c(c(x1))))
     c(c(x1)) -> a(b(x1))
    graph:
     c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(a(c(c(x1))))
     c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> a#(c(c(x1)))
     c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(c(x1))
     c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(x1)
     b#(a(a(x1))) -> c#(c(x1)) -> c#(c(x1)) -> a#(b(x1))
     b#(a(a(x1))) -> c#(c(x1)) -> c#(c(x1)) -> b#(x1)
     b#(a(a(x1))) -> c#(a(c(c(x1)))) -> c#(c(x1)) -> a#(b(x1))
     b#(a(a(x1))) -> c#(a(c(c(x1)))) -> c#(c(x1)) -> b#(x1)
     b#(a(a(x1))) -> c#(x1) -> c#(c(x1)) -> a#(b(x1))
     b#(a(a(x1))) -> c#(x1) -> c#(c(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 10/36
     DPs:
      c#(c(x1)) -> b#(x1)
      b#(a(a(x1))) -> c#(x1)
      b#(a(a(x1))) -> c#(c(x1))
      b#(a(a(x1))) -> c#(a(c(c(x1))))
     TRS:
      a(x1) -> x1
      b(a(a(x1))) -> c(a(c(c(x1))))
      c(c(x1)) -> a(b(x1))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       b(a(a(x1))) -> c(a(c(c(x1))))
       c(c(x1)) -> a(b(x1))
      interpretation:
       [b#](x0) = [0 0]x0 + [1],
       
                 [-& 0 ]     [0 ]
       [b](x0) = [0  0 ]x0 + [-&],
       
       [c#](x0) = [0 0]x0 + [0],
       
                 [0 0]     [1]
       [a](x0) = [2 2]x0 + [3],
       
                 [0 0]     [1]
       [c](x0) = [2 0]x0 + [0]
      orientation:
       c#(c(x1)) = [2 0]x1 + [1] >= [0 0]x1 + [1] = b#(x1)
       
       b#(a(a(x1))) = [4 4]x1 + [5] >= [0 0]x1 + [0] = c#(x1)
       
       b#(a(a(x1))) = [4 4]x1 + [5] >= [2 0]x1 + [1] = c#(c(x1))
       
       b#(a(a(x1))) = [4 4]x1 + [5] >= [4 4]x1 + [5] = c#(a(c(c(x1))))
       
               [0 0]     [1]           
       a(x1) = [2 2]x1 + [3] >= x1 = x1
       
                     [4 4]     [5]    [4 4]     [5]                 
       b(a(a(x1))) = [4 4]x1 + [5] >= [4 4]x1 + [5] = c(a(c(c(x1))))
       
                  [2 0]     [1]    [0 0]     [1]           
       c(c(x1)) = [2 2]x1 + [3] >= [2 2]x1 + [3] = a(b(x1))
      problem:
       DPs:
        c#(c(x1)) -> b#(x1)
        b#(a(a(x1))) -> c#(a(c(c(x1))))
       TRS:
        a(x1) -> x1
        b(a(a(x1))) -> c(a(c(c(x1))))
        c(c(x1)) -> a(b(x1))
      Restore Modifier:
       DPs:
        c#(c(x1)) -> b#(x1)
        b#(a(a(x1))) -> c#(a(c(c(x1))))
       TRS:
        a(x1) -> x1
        b(a(a(x1))) -> c(a(c(c(x1))))
        c(c(x1)) -> a(b(x1))
       EDG Processor:
        DPs:
         c#(c(x1)) -> b#(x1)
         b#(a(a(x1))) -> c#(a(c(c(x1))))
        TRS:
         a(x1) -> x1
         b(a(a(x1))) -> c(a(c(c(x1))))
         c(c(x1)) -> a(b(x1))
        graph:
         c#(c(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(a(c(c(x1))))
         b#(a(a(x1))) -> c#(a(c(c(x1)))) -> c#(c(x1)) -> b#(x1)
        Arctic Interpretation Processor:
         dimension: 2
         usable rules:
          a(x1) -> x1
          b(a(a(x1))) -> c(a(c(c(x1))))
          c(c(x1)) -> a(b(x1))
         interpretation:
          [b#](x0) = [0  -&]x0 + [0],
          
                    [0  -&]     [-&]
          [b](x0) = [2  0 ]x0 + [0 ],
          
          [c#](x0) = [-& 0 ]x0 + [1],
          
                    [2 0]     [0]
          [a](x0) = [0 0]x0 + [0],
          
                    [-& 0 ]     [0]
          [c](x0) = [2  0 ]x0 + [0]
         orientation:
          c#(c(x1)) = [2 0]x1 + [1] >= [0  -&]x1 + [0] = b#(x1)
          
          b#(a(a(x1))) = [4 2]x1 + [2] >= [2 2]x1 + [2] = c#(a(c(c(x1))))
          
                  [2 0]     [0]           
          a(x1) = [0 0]x1 + [0] >= x1 = x1
          
                        [4 2]     [2]    [2 2]     [2]                 
          b(a(a(x1))) = [6 4]x1 + [4] >= [6 4]x1 + [4] = c(a(c(c(x1))))
          
                     [2 0]     [0]    [2 0]     [0]           
          c(c(x1)) = [2 2]x1 + [2] >= [2 0]x1 + [0] = a(b(x1))
         problem:
          DPs:
           b#(a(a(x1))) -> c#(a(c(c(x1))))
          TRS:
           a(x1) -> x1
           b(a(a(x1))) -> c(a(c(c(x1))))
           c(c(x1)) -> a(b(x1))
         Restore Modifier:
          DPs:
           b#(a(a(x1))) -> c#(a(c(c(x1))))
          TRS:
           a(x1) -> x1
           b(a(a(x1))) -> c(a(c(c(x1))))
           c(c(x1)) -> a(b(x1))
          EDG Processor:
           DPs:
            b#(a(a(x1))) -> c#(a(c(c(x1))))
           TRS:
            a(x1) -> x1
            b(a(a(x1))) -> c(a(c(c(x1))))
            c(c(x1)) -> a(b(x1))
           graph:
            
           SCC Processor:
            #sccs: 0
            #rules: 0
            #arcs: 0/1