YES

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

Proof:
 String Reversal Processor:
  a(x1) -> b(x1)
  b(b(a(x1))) -> c(x1)
  c(a(x1)) -> a(a(b(c(x1))))
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    b#(b(a(x1))) -> c#(x1)
    c#(a(x1)) -> c#(x1)
    c#(a(x1)) -> b#(c(x1))
    c#(a(x1)) -> a#(b(c(x1)))
    c#(a(x1)) -> a#(a(b(c(x1))))
   TRS:
    a(x1) -> b(x1)
    b(b(a(x1))) -> c(x1)
    c(a(x1)) -> a(a(b(c(x1))))
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     b#(b(a(x1))) -> c#(x1)
     c#(a(x1)) -> c#(x1)
     c#(a(x1)) -> b#(c(x1))
     c#(a(x1)) -> a#(b(c(x1)))
     c#(a(x1)) -> a#(a(b(c(x1))))
    TRS:
     a(x1) -> b(x1)
     b(b(a(x1))) -> c(x1)
     c(a(x1)) -> a(a(b(c(x1))))
    graph:
     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(a(b(c(x1))))
     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(b(c(x1)))
     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(c(x1))
     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
     c#(a(x1)) -> b#(c(x1)) -> b#(b(a(x1))) -> c#(x1)
     c#(a(x1)) -> a#(b(c(x1))) -> a#(x1) -> b#(x1)
     c#(a(x1)) -> a#(a(b(c(x1)))) -> a#(x1) -> b#(x1)
     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(a(b(c(x1))))
     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(b(c(x1)))
     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> b#(c(x1))
     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1)
     a#(x1) -> b#(x1) -> b#(b(a(x1))) -> c#(x1)
    Arctic Interpretation Processor:
     dimension: 3
     usable rules:
      a(x1) -> b(x1)
      b(b(a(x1))) -> c(x1)
      c(a(x1)) -> a(a(b(c(x1))))
     interpretation:
      [c#](x0) = [-& -& 0 ]x0 + [0],
      
      [b#](x0) = [-& 0  0 ]x0 + [0],
      
      [a#](x0) = [-& 0  0 ]x0 + [1],
      
                [0  0  1 ]     [1 ]
      [c](x0) = [-& -& 0 ]x0 + [-&]
                [0  0  1 ]     [0 ],
      
                [-& 0  -&]     [1 ]
      [b](x0) = [-& -& 0 ]x0 + [0 ]
                [-& 0  -&]     [-&],
      
                [0  1  0 ]     [1]
      [a](x0) = [-& -& 0 ]x0 + [1]
                [0  0  1 ]     [1]
     orientation:
      a#(x1) = [-& 0  0 ]x1 + [1] >= [-& 0  0 ]x1 + [0] = b#(x1)
      
      b#(b(a(x1))) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = c#(x1)
      
      c#(a(x1)) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = c#(x1)
      
      c#(a(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [0] = b#(c(x1))
      
      c#(a(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = a#(b(c(x1)))
      
      c#(a(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = a#(a(b(c(x1))))
      
              [0  1  0 ]     [1]    [-& 0  -&]     [1 ]        
      a(x1) = [-& -& 0 ]x1 + [1] >= [-& -& 0 ]x1 + [0 ] = b(x1)
              [0  0  1 ]     [1]    [-& 0  -&]     [-&]        
      
                    [0  0  1 ]     [1]    [0  0  1 ]     [1 ]        
      b(b(a(x1))) = [-& -& 0 ]x1 + [1] >= [-& -& 0 ]x1 + [-&] = c(x1)
                    [0  0  1 ]     [1]    [0  0  1 ]     [0 ]        
      
                 [1 1 2]     [2]    [1 1 2]     [2]                 
      c(a(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = a(a(b(c(x1))))
                 [1 1 2]     [2]    [1 1 2]     [2]                 
     problem:
      DPs:
       a#(x1) -> b#(x1)
       c#(a(x1)) -> b#(c(x1))
       c#(a(x1)) -> a#(b(c(x1)))
       c#(a(x1)) -> a#(a(b(c(x1))))
      TRS:
       a(x1) -> b(x1)
       b(b(a(x1))) -> c(x1)
       c(a(x1)) -> a(a(b(c(x1))))
     Restore Modifier:
      DPs:
       a#(x1) -> b#(x1)
       c#(a(x1)) -> b#(c(x1))
       c#(a(x1)) -> a#(b(c(x1)))
       c#(a(x1)) -> a#(a(b(c(x1))))
      TRS:
       a(x1) -> b(x1)
       b(b(a(x1))) -> c(x1)
       c(a(x1)) -> a(a(b(c(x1))))
      EDG Processor:
       DPs:
        a#(x1) -> b#(x1)
        c#(a(x1)) -> b#(c(x1))
        c#(a(x1)) -> a#(b(c(x1)))
        c#(a(x1)) -> a#(a(b(c(x1))))
       TRS:
        a(x1) -> b(x1)
        b(b(a(x1))) -> c(x1)
        c(a(x1)) -> a(a(b(c(x1))))
       graph:
        c#(a(x1)) -> a#(b(c(x1))) -> a#(x1) -> b#(x1)
        c#(a(x1)) -> a#(a(b(c(x1)))) -> a#(x1) -> b#(x1)
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 2/16