YES

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

Proof:
 String Reversal Processor:
  a(a(x1)) -> b(a(x1))
  c(a(x1)) -> b(x1)
  b(b(x1)) -> a(b(c(x1)))
  DP Processor:
   DPs:
    a#(a(x1)) -> b#(a(x1))
    c#(a(x1)) -> b#(x1)
    b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> b#(c(x1))
    b#(b(x1)) -> a#(b(c(x1)))
   TRS:
    a(a(x1)) -> b(a(x1))
    c(a(x1)) -> b(x1)
    b(b(x1)) -> a(b(c(x1)))
   TDG Processor:
    DPs:
     a#(a(x1)) -> b#(a(x1))
     c#(a(x1)) -> b#(x1)
     b#(b(x1)) -> c#(x1)
     b#(b(x1)) -> b#(c(x1))
     b#(b(x1)) -> a#(b(c(x1)))
    TRS:
     a(a(x1)) -> b(a(x1))
     c(a(x1)) -> b(x1)
     b(b(x1)) -> a(b(c(x1)))
    graph:
     c#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(b(c(x1)))
     c#(a(x1)) -> b#(x1) -> b#(b(x1)) -> b#(c(x1))
     c#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(x1)
     b#(b(x1)) -> c#(x1) -> c#(a(x1)) -> b#(x1)
     b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> a#(b(c(x1)))
     b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> b#(c(x1))
     b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> c#(x1)
     b#(b(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1))
     a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(b(c(x1)))
     a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> b#(c(x1))
     a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> c#(x1)
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      a(a(x1)) -> b(a(x1))
      c(a(x1)) -> b(x1)
      b(b(x1)) -> a(b(c(x1)))
     interpretation:
      [b#](x0) = 8x0,
      
      [b](x0) = 2x0 + 8,
      
      [a#](x0) = 8x0 + 0,
      
      [c#](x0) = 9x0 + 1,
      
      [a](x0) = 2x0 + 8,
      
      [c](x0) = x0 + 6
     orientation:
      a#(a(x1)) = 10x1 + 16 >= 10x1 + 16 = b#(a(x1))
      
      c#(a(x1)) = 11x1 + 17 >= 8x1 = b#(x1)
      
      b#(b(x1)) = 10x1 + 16 >= 9x1 + 1 = c#(x1)
      
      b#(b(x1)) = 10x1 + 16 >= 8x1 + 14 = b#(c(x1))
      
      b#(b(x1)) = 10x1 + 16 >= 10x1 + 16 = a#(b(c(x1)))
      
      a(a(x1)) = 4x1 + 10 >= 4x1 + 10 = b(a(x1))
      
      c(a(x1)) = 2x1 + 8 >= 2x1 + 8 = b(x1)
      
      b(b(x1)) = 4x1 + 10 >= 4x1 + 10 = a(b(c(x1)))
     problem:
      DPs:
       a#(a(x1)) -> b#(a(x1))
       b#(b(x1)) -> a#(b(c(x1)))
      TRS:
       a(a(x1)) -> b(a(x1))
       c(a(x1)) -> b(x1)
       b(b(x1)) -> a(b(c(x1)))
     Restore Modifier:
      DPs:
       a#(a(x1)) -> b#(a(x1))
       b#(b(x1)) -> a#(b(c(x1)))
      TRS:
       a(a(x1)) -> b(a(x1))
       c(a(x1)) -> b(x1)
       b(b(x1)) -> a(b(c(x1)))
      EDG Processor:
       DPs:
        a#(a(x1)) -> b#(a(x1))
        b#(b(x1)) -> a#(b(c(x1)))
       TRS:
        a(a(x1)) -> b(a(x1))
        c(a(x1)) -> b(x1)
        b(b(x1)) -> a(b(c(x1)))
       graph:
        b#(b(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1))
        a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(b(c(x1)))
       Arctic Interpretation Processor:
        dimension: 2
        usable rules:
         a(a(x1)) -> b(a(x1))
         c(a(x1)) -> b(x1)
         b(b(x1)) -> a(b(c(x1)))
        interpretation:
         [b#](x0) = [-& 0 ]x0 + [0],
         
                   [0  0 ]     [-&]
         [b](x0) = [2  -&]x0 + [0 ],
         
         [a#](x0) = [0  -&]x0,
         
                   [2 0]     [0]
         [a](x0) = [2 0]x0 + [0],
         
                   [0  -&]  
         [c](x0) = [0  -&]x0
        orientation:
         a#(a(x1)) = [2 0]x1 + [0] >= [2 0]x1 + [0] = b#(a(x1))
         
         b#(b(x1)) = [2  -&]x1 + [0] >= [0  -&]x1 = a#(b(c(x1)))
         
                    [4 2]     [2]    [2 0]     [0]           
         a(a(x1)) = [4 2]x1 + [2] >= [4 2]x1 + [2] = b(a(x1))
         
                    [2 0]     [0]    [0  0 ]     [-&]        
         c(a(x1)) = [2 0]x1 + [0] >= [2  -&]x1 + [0 ] = b(x1)
         
                    [2 0]     [0]    [2  -&]     [0]              
         b(b(x1)) = [2 2]x1 + [0] >= [2  -&]x1 + [0] = a(b(c(x1)))
        problem:
         DPs:
          a#(a(x1)) -> b#(a(x1))
         TRS:
          a(a(x1)) -> b(a(x1))
          c(a(x1)) -> b(x1)
          b(b(x1)) -> a(b(c(x1)))
        Restore Modifier:
         DPs:
          a#(a(x1)) -> b#(a(x1))
         TRS:
          a(a(x1)) -> b(a(x1))
          c(a(x1)) -> b(x1)
          b(b(x1)) -> a(b(c(x1)))
         EDG Processor:
          DPs:
           a#(a(x1)) -> b#(a(x1))
          TRS:
           a(a(x1)) -> b(a(x1))
           c(a(x1)) -> b(x1)
           b(b(x1)) -> a(b(c(x1)))
          graph:
           
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 0/1