YES

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

Proof:
 DP Processor:
  DPs:
   c#(b(x1)) -> c#(x1)
   c#(b(x1)) -> c#(c(x1))
   c#(b(x1)) -> a#(c(c(x1)))
   c#(b(x1)) -> a#(a(c(c(x1))))
  TRS:
   a(b(x1)) -> x1
   a(c(x1)) -> b(b(x1))
   c(b(x1)) -> a(a(c(c(x1))))
  TDG Processor:
   DPs:
    c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> c#(c(x1))
    c#(b(x1)) -> a#(c(c(x1)))
    c#(b(x1)) -> a#(a(c(c(x1))))
   TRS:
    a(b(x1)) -> x1
    a(c(x1)) -> b(b(x1))
    c(b(x1)) -> a(a(c(c(x1))))
   graph:
    c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(a(c(c(x1))))
    c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(c(c(x1)))
    c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(c(x1))
    c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(a(c(c(x1))))
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(c(x1)))
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(c(x1))
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 8/16
    DPs:
     c#(b(x1)) -> c#(c(x1))
     c#(b(x1)) -> c#(x1)
    TRS:
     a(b(x1)) -> x1
     a(c(x1)) -> b(b(x1))
     c(b(x1)) -> a(a(c(c(x1))))
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
      [c#](x0) = [1 0]x0,
      
                [1 0]     [-&]
      [c](x0) = [2 1]x0 + [0 ],
      
                [-& 0 ]     [0]
      [a](x0) = [0  -&]x0 + [0],
      
                [1 0]     [-&]
      [b](x0) = [0 0]x0 + [0 ]
     orientation:
      c#(b(x1)) = [2 1]x1 + [0] >= [2 1]x1 + [0] = c#(c(x1))
      
      c#(b(x1)) = [2 1]x1 + [0] >= [1 0]x1 = c#(x1)
      
                 [0 0]     [0]           
      a(b(x1)) = [1 0]x1 + [0] >= x1 = x1
      
                 [2 1]     [0]    [2 1]     [0]           
      a(c(x1)) = [1 0]x1 + [0] >= [1 0]x1 + [0] = b(b(x1))
      
                 [2 1]     [0]    [2 1]     [0]                 
      c(b(x1)) = [3 2]x1 + [1] >= [3 2]x1 + [1] = a(a(c(c(x1))))
     problem:
      DPs:
       c#(b(x1)) -> c#(c(x1))
      TRS:
       a(b(x1)) -> x1
       a(c(x1)) -> b(b(x1))
       c(b(x1)) -> a(a(c(c(x1))))
     EDG Processor:
      DPs:
       c#(b(x1)) -> c#(c(x1))
      TRS:
       a(b(x1)) -> x1
       a(c(x1)) -> b(b(x1))
       c(b(x1)) -> a(a(c(c(x1))))
      graph:
       c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(c(x1))
      Arctic Interpretation Processor:
       dimension: 3
       interpretation:
        [c#](x0) = [0 0 1]x0 + [0],
        
                  [0  0  0 ]     [0 ]
        [c](x0) = [0  0  1 ]x0 + [0 ]
                  [-& -& 0 ]     [-&],
        
                  [0  0  -&]     [0 ]
        [a](x0) = [-& -& 0 ]x0 + [-&]
                  [0  1  -&]     [0 ],
        
                  [0  0  0 ]     [-&]
        [b](x0) = [-& -& -&]x0 + [-&]
                  [0  0  1 ]     [0 ]
       orientation:
        c#(b(x1)) = [1 1 2]x1 + [1] >= [0 0 1]x1 + [0] = c#(c(x1))
        
                   [0 0 0]     [0]           
        a(b(x1)) = [0 0 1]x1 + [0] >= x1 = x1
                   [0 0 0]     [0]           
        
                   [0  0  1 ]     [0 ]    [0  0  1 ]     [0 ]           
        a(c(x1)) = [-& -& 0 ]x1 + [-&] >= [-& -& -&]x1 + [-&] = b(b(x1))
                   [1  1  2 ]     [1 ]    [1  1  2 ]     [1 ]           
        
                   [0 0 1]     [0]    [0 0 1]     [0]                 
        c(b(x1)) = [1 1 2]x1 + [1] >= [1 1 2]x1 + [1] = a(a(c(c(x1))))
                   [0 0 1]     [0]    [0 0 1]     [0]                 
       problem:
        DPs:
         
        TRS:
         a(b(x1)) -> x1
         a(c(x1)) -> b(b(x1))
         c(b(x1)) -> a(a(c(c(x1))))
       Qed