YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> c#(x1)
   c#(c(x1)) -> a#(c(x1))
   c#(c(x1)) -> a#(a(c(x1)))
   c#(c(x1)) -> b#(a(a(c(x1))))
   c#(c(x1)) -> b#(b(a(a(c(x1)))))
  TRS:
   a(x1) -> x1
   a(b(x1)) -> c(x1)
   b(x1) -> x1
   c(c(x1)) -> b(b(a(a(c(x1)))))
  TDG Processor:
   DPs:
    a#(b(x1)) -> c#(x1)
    c#(c(x1)) -> a#(c(x1))
    c#(c(x1)) -> a#(a(c(x1)))
    c#(c(x1)) -> b#(a(a(c(x1))))
    c#(c(x1)) -> b#(b(a(a(c(x1)))))
   TRS:
    a(x1) -> x1
    a(b(x1)) -> c(x1)
    b(x1) -> x1
    c(c(x1)) -> b(b(a(a(c(x1)))))
   graph:
    c#(c(x1)) -> a#(c(x1)) -> a#(b(x1)) -> c#(x1)
    c#(c(x1)) -> a#(a(c(x1))) -> a#(b(x1)) -> c#(x1)
    a#(b(x1)) -> c#(x1) -> c#(c(x1)) -> b#(b(a(a(c(x1)))))
    a#(b(x1)) -> c#(x1) -> c#(c(x1)) -> b#(a(a(c(x1))))
    a#(b(x1)) -> c#(x1) -> c#(c(x1)) -> a#(a(c(x1)))
    a#(b(x1)) -> c#(x1) -> c#(c(x1)) -> a#(c(x1))
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 6/25
    DPs:
     c#(c(x1)) -> a#(c(x1))
     a#(b(x1)) -> c#(x1)
     c#(c(x1)) -> a#(a(c(x1)))
    TRS:
     a(x1) -> x1
     a(b(x1)) -> c(x1)
     b(x1) -> x1
     c(c(x1)) -> b(b(a(a(c(x1)))))
    Arctic Interpretation Processor:
     dimension: 3
     usable rules:
      a(x1) -> x1
      a(b(x1)) -> c(x1)
      b(x1) -> x1
      c(c(x1)) -> b(b(a(a(c(x1)))))
     interpretation:
      [c#](x0) = [-& -& 0 ]x0 + [0],
      
      [a#](x0) = [-& 0  0 ]x0 + [0],
      
                [-& 0  1 ]     [0]
      [c](x0) = [-& -& 1 ]x0 + [0]
                [0  0  1 ]     [0],
      
                [0  0  1 ]     [0]
      [b](x0) = [0  0  1 ]x0 + [1]
                [-& 0  0 ]     [0],
      
                [0  0  0 ]     [0]
      [a](x0) = [0  0  -&]x0 + [0]
                [-& 0  0 ]     [0]
     orientation:
      c#(c(x1)) = [0 0 1]x1 + [0] >= [0 0 1]x1 + [0] = a#(c(x1))
      
      a#(b(x1)) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = c#(x1)
      
      c#(c(x1)) = [0 0 1]x1 + [0] >= [0 0 1]x1 + [0] = a#(a(c(x1)))
      
              [0  0  0 ]     [0]           
      a(x1) = [0  0  -&]x1 + [0] >= x1 = x1
              [-& 0  0 ]     [0]           
      
                 [0 0 1]     [1]    [-& 0  1 ]     [0]        
      a(b(x1)) = [0 0 1]x1 + [1] >= [-& -& 1 ]x1 + [0] = c(x1)
                 [0 0 1]     [1]    [0  0  1 ]     [0]        
      
              [0  0  1 ]     [0]           
      b(x1) = [0  0  1 ]x1 + [1] >= x1 = x1
              [-& 0  0 ]     [0]           
      
                 [1 1 2]     [1]    [1 1 2]     [1]                    
      c(c(x1)) = [1 1 2]x1 + [1] >= [1 1 2]x1 + [1] = b(b(a(a(c(x1)))))
                 [1 1 2]     [1]    [1 1 2]     [1]                    
     problem:
      DPs:
       c#(c(x1)) -> a#(c(x1))
       c#(c(x1)) -> a#(a(c(x1)))
      TRS:
       a(x1) -> x1
       a(b(x1)) -> c(x1)
       b(x1) -> x1
       c(c(x1)) -> b(b(a(a(c(x1)))))
     Restore Modifier:
      DPs:
       c#(c(x1)) -> a#(c(x1))
       c#(c(x1)) -> a#(a(c(x1)))
      TRS:
       a(x1) -> x1
       a(b(x1)) -> c(x1)
       b(x1) -> x1
       c(c(x1)) -> b(b(a(a(c(x1)))))
      EDG Processor:
       DPs:
        c#(c(x1)) -> a#(c(x1))
        c#(c(x1)) -> a#(a(c(x1)))
       TRS:
        a(x1) -> x1
        a(b(x1)) -> c(x1)
        b(x1) -> x1
        c(c(x1)) -> b(b(a(a(c(x1)))))
       graph:
        
       Qed