YES

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

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