YES

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

Proof:
 String Reversal Processor:
  a(x1) -> b(x1)
  a(a(x1)) -> c(a(b(a(x1))))
  b(b(c(x1))) -> a(x1)
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(a(x1)) -> b#(a(x1))
    a#(a(x1)) -> a#(b(a(x1)))
    b#(b(c(x1))) -> a#(x1)
   TRS:
    a(x1) -> b(x1)
    a(a(x1)) -> c(a(b(a(x1))))
    b(b(c(x1))) -> a(x1)
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     a#(a(x1)) -> b#(a(x1))
     a#(a(x1)) -> a#(b(a(x1)))
     b#(b(c(x1))) -> a#(x1)
    TRS:
     a(x1) -> b(x1)
     a(a(x1)) -> c(a(b(a(x1))))
     b(b(c(x1))) -> a(x1)
    graph:
     b#(b(c(x1))) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1)))
     b#(b(c(x1))) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
     b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
     a#(a(x1)) -> b#(a(x1)) -> b#(b(c(x1))) -> a#(x1)
     a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1)))
     a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1))
     a#(a(x1)) -> a#(b(a(x1))) -> a#(x1) -> b#(x1)
     a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1)
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> b(x1)
      a(a(x1)) -> c(a(b(a(x1))))
      b(b(c(x1))) -> a(x1)
     interpretation:
      [b#](x0) = [0 2]x0 + [0],
      
                [-& 0 ]     [0 ]
      [b](x0) = [0  -&]x0 + [-&],
      
      [a#](x0) = [0 2]x0 + [0],
      
                [-& 0 ]     [0]
      [a](x0) = [0  2 ]x0 + [2],
      
                [0 0]     [2]
      [c](x0) = [0 2]x0 + [2]
     orientation:
      a#(x1) = [0 2]x1 + [0] >= [0 2]x1 + [0] = b#(x1)
      
      a#(a(x1)) = [2 4]x1 + [4] >= [2 4]x1 + [4] = b#(a(x1))
      
      a#(a(x1)) = [2 4]x1 + [4] >= [0 2]x1 + [2] = a#(b(a(x1)))
      
      b#(b(c(x1))) = [2 2]x1 + [4] >= [0 2]x1 + [0] = a#(x1)
      
              [-& 0 ]     [0]    [-& 0 ]     [0 ]        
      a(x1) = [0  2 ]x1 + [2] >= [0  -&]x1 + [-&] = b(x1)
      
                 [0 2]     [2]    [0 2]     [2]                 
      a(a(x1)) = [2 4]x1 + [4] >= [2 4]x1 + [4] = c(a(b(a(x1))))
      
                    [0 0]     [2]    [-& 0 ]     [0]        
      b(b(c(x1))) = [0 2]x1 + [2] >= [0  2 ]x1 + [2] = a(x1)
     problem:
      DPs:
       a#(x1) -> b#(x1)
       a#(a(x1)) -> b#(a(x1))
       b#(b(c(x1))) -> a#(x1)
      TRS:
       a(x1) -> b(x1)
       a(a(x1)) -> c(a(b(a(x1))))
       b(b(c(x1))) -> a(x1)
     Restore Modifier:
      DPs:
       a#(x1) -> b#(x1)
       a#(a(x1)) -> b#(a(x1))
       b#(b(c(x1))) -> a#(x1)
      TRS:
       a(x1) -> b(x1)
       a(a(x1)) -> c(a(b(a(x1))))
       b(b(c(x1))) -> a(x1)
      EDG Processor:
       DPs:
        a#(x1) -> b#(x1)
        a#(a(x1)) -> b#(a(x1))
        b#(b(c(x1))) -> a#(x1)
       TRS:
        a(x1) -> b(x1)
        a(a(x1)) -> c(a(b(a(x1))))
        b(b(c(x1))) -> a(x1)
       graph:
        b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
        b#(b(c(x1))) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
        a#(a(x1)) -> b#(a(x1)) -> b#(b(c(x1))) -> a#(x1)
        a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1)
       Matrix Interpretation Processor: dim=1
        
        usable rules:
         a(x1) -> b(x1)
         a(a(x1)) -> c(a(b(a(x1))))
         b(b(c(x1))) -> a(x1)
        interpretation:
         [b#](x0) = x0 + 15/2,
         
         [b](x0) = 2x0,
         
         [a#](x0) = x0 + 15/2,
         
         [a](x0) = 2x0 + 9/2,
         
         [c](x0) = 1/2x0 + 3/2
        orientation:
         a#(x1) = x1 + 15/2 >= x1 + 15/2 = b#(x1)
         
         a#(a(x1)) = 2x1 + 12 >= 2x1 + 12 = b#(a(x1))
         
         b#(b(c(x1))) = x1 + 21/2 >= x1 + 15/2 = a#(x1)
         
         a(x1) = 2x1 + 9/2 >= 2x1 = b(x1)
         
         a(a(x1)) = 4x1 + 27/2 >= 4x1 + 51/4 = c(a(b(a(x1))))
         
         b(b(c(x1))) = 2x1 + 6 >= 2x1 + 9/2 = a(x1)
        problem:
         DPs:
          a#(x1) -> b#(x1)
          a#(a(x1)) -> b#(a(x1))
         TRS:
          a(x1) -> b(x1)
          a(a(x1)) -> c(a(b(a(x1))))
          b(b(c(x1))) -> a(x1)
        Restore Modifier:
         DPs:
          a#(x1) -> b#(x1)
          a#(a(x1)) -> b#(a(x1))
         TRS:
          a(x1) -> b(x1)
          a(a(x1)) -> c(a(b(a(x1))))
          b(b(c(x1))) -> a(x1)
         EDG Processor:
          DPs:
           a#(x1) -> b#(x1)
           a#(a(x1)) -> b#(a(x1))
          TRS:
           a(x1) -> b(x1)
           a(a(x1)) -> c(a(b(a(x1))))
           b(b(c(x1))) -> a(x1)
          graph:
           
          SCC Processor:
           #sccs: 0
           #rules: 0
           #arcs: 0/4