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: 1
      interpretation:
       [c#](x0) = x0,
       
       [b#](x0) = 1x0 + 0,
       
       [c](x0) = x0,
       
       [b](x0) = 1x0 + 0,
       
       [a](x0) = x0 + -1
      orientation:
       c#(b(x1)) = 1x1 + 0 >= 1x1 + 0 = b#(a(x1))
       
       b#(a(a(x1))) = 1x1 + 0 >= x1 = c#(x1)
       
       b#(a(a(x1))) = 1x1 + 0 >= x1 = c#(c(x1))
       
       b#(a(a(x1))) = 1x1 + 0 >= 1x1 + 0 = b#(c(c(x1)))
       
       a(x1) = x1 + -1 >= x1 = x1
       
       b(a(a(x1))) = 1x1 + 0 >= 1x1 + 0 = a(b(c(c(x1))))
       
       c(b(x1)) = 1x1 + 0 >= 1x1 + 0 = b(a(x1))
      problem:
       DPs:
        c#(b(x1)) -> b#(a(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:
        c#(b(x1)) -> b#(a(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:
        c#(b(x1)) -> b#(a(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)))
       SCC Processor:
        #sccs: 1
        #rules: 1
        #arcs: 2/4
        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))
        Arctic Interpretation Processor:
         dimension: 4
         interpretation:
          [b#](x0) = [0 1 0 0]x0 + [0],
          
                    [-& 0  0  0 ]     [0 ]
                    [-& -& -& -&]     [-&]
          [c](x0) = [-& 0  0  0 ]x0 + [0 ]
                    [-& 0  0  0 ]     [0 ],
          
                    [0  0  0  0 ]     [1 ]
                    [-& -& -& -&]     [-&]
          [b](x0) = [1  0  1  1 ]x0 + [1 ]
                    [-& 1  -& -&]     [-&],
          
                    [0  0  -& 0 ]     [0 ]
                    [-& 0  -& 0 ]     [-&]
          [a](x0) = [0  0  0  0 ]x0 + [0 ]
                    [-& 0  0  0 ]     [0 ]
         orientation:
          b#(a(a(x1))) = [0 1 1 1]x1 + [1] >= [-& 0  0  0 ]x1 + [0] = b#(c(c(x1)))
          
                  [0  0  -& 0 ]     [0 ]           
                  [-& 0  -& 0 ]     [-&]           
          a(x1) = [0  0  0  0 ]x1 + [0 ] >= x1 = x1
                  [-& 0  0  0 ]     [0 ]           
          
                        [0  0  0  0 ]     [1 ]    [-& 0  0  0 ]     [1 ]                 
                        [-& -& -& -&]     [-&]    [-& -& -& -&]     [-&]                 
          b(a(a(x1))) = [1  1  1  1 ]x1 + [1 ] >= [-& 1  1  1 ]x1 + [1 ] = a(b(c(c(x1))))
                        [-& 1  1  1 ]     [1 ]    [-& 1  1  1 ]     [1 ]                 
          
                     [1  1  1  1 ]     [1 ]    [0  0  0  0 ]     [1 ]           
                     [-& -& -& -&]     [-&]    [-& -& -& -&]     [-&]           
          c(b(x1)) = [1  1  1  1 ]x1 + [1 ] >= [1  1  1  1 ]x1 + [1 ] = b(a(x1))
                     [1  1  1  1 ]     [1 ]    [-& 1  -& 1 ]     [-&]           
         problem:
          DPs:
           
          TRS:
           a(x1) -> x1
           b(a(a(x1))) -> a(b(c(c(x1))))
           c(b(x1)) -> b(a(x1))
         Qed