YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> c#(a(x1))
   a#(b(x1)) -> a#(c(a(x1)))
   a#(b(x1)) -> c#(a(c(a(x1))))
  TRS:
   a(x1) -> b(x1)
   a(b(x1)) -> c(a(c(a(x1))))
   c(b(c(x1))) -> b(x1)
  TDG Processor:
   DPs:
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> c#(a(x1))
    a#(b(x1)) -> a#(c(a(x1)))
    a#(b(x1)) -> c#(a(c(a(x1))))
   TRS:
    a(x1) -> b(x1)
    a(b(x1)) -> c(a(c(a(x1))))
    c(b(c(x1))) -> b(x1)
   graph:
    a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> c#(a(c(a(x1))))
    a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> a#(c(a(x1)))
    a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> c#(a(x1))
    a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(a(c(a(x1))))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(c(a(x1)))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(a(x1))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 8/16
    DPs:
     a#(b(x1)) -> a#(c(a(x1)))
     a#(b(x1)) -> a#(x1)
    TRS:
     a(x1) -> b(x1)
     a(b(x1)) -> c(a(c(a(x1))))
     c(b(c(x1))) -> b(x1)
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> b(x1)
      a(b(x1)) -> c(a(c(a(x1))))
      c(b(c(x1))) -> b(x1)
     interpretation:
      [a#](x0) = [0 0]x0 + [0],
      
                [0  0 ]     [0]
      [c](x0) = [-& 0 ]x0 + [3],
      
                [3 2]     [3 ]
      [b](x0) = [1 0]x0 + [-&],
      
                [3 2]     [3]
      [a](x0) = [2 2]x0 + [0]
     orientation:
      a#(b(x1)) = [3 2]x1 + [3] >= [3 2]x1 + [3] = a#(c(a(x1)))
      
      a#(b(x1)) = [3 2]x1 + [3] >= [0 0]x1 + [0] = a#(x1)
      
              [3 2]     [3]    [3 2]     [3 ]        
      a(x1) = [2 2]x1 + [0] >= [1 0]x1 + [-&] = b(x1)
      
                 [6 5]     [6]    [6 5]     [6]                 
      a(b(x1)) = [5 4]x1 + [5] >= [5 4]x1 + [5] = c(a(c(a(x1))))
      
                    [3 3]     [5]    [3 2]     [3 ]        
      c(b(c(x1))) = [1 1]x1 + [3] >= [1 0]x1 + [-&] = b(x1)
     problem:
      DPs:
       a#(b(x1)) -> a#(c(a(x1)))
      TRS:
       a(x1) -> b(x1)
       a(b(x1)) -> c(a(c(a(x1))))
       c(b(c(x1))) -> b(x1)
     Restore Modifier:
      DPs:
       a#(b(x1)) -> a#(c(a(x1)))
      TRS:
       a(x1) -> b(x1)
       a(b(x1)) -> c(a(c(a(x1))))
       c(b(c(x1))) -> b(x1)
      EDG Processor:
       DPs:
        a#(b(x1)) -> a#(c(a(x1)))
       TRS:
        a(x1) -> b(x1)
        a(b(x1)) -> c(a(c(a(x1))))
        c(b(c(x1))) -> b(x1)
       graph:
        a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> a#(c(a(x1)))
       Arctic Interpretation Processor:
        dimension: 2
        usable rules:
         a(x1) -> b(x1)
         a(b(x1)) -> c(a(c(a(x1))))
         c(b(c(x1))) -> b(x1)
        interpretation:
         [a#](x0) = [-& 0 ]x0 + [0],
         
                   [1  -&]     [1]
         [c](x0) = [-& -1]x0 + [0],
         
                   [-& 0 ]     [0]
         [b](x0) = [1  -&]x0 + [1],
         
                   [-& 0 ]     [0]
         [a](x0) = [1  -&]x0 + [1]
        orientation:
         a#(b(x1)) = [1  -&]x1 + [1] >= [0  -&]x1 + [0] = a#(c(a(x1)))
         
                 [-& 0 ]     [0]    [-& 0 ]     [0]        
         a(x1) = [1  -&]x1 + [1] >= [1  -&]x1 + [1] = b(x1)
         
                    [1  -&]     [1]    [1  -&]     [1]                 
         a(b(x1)) = [-& 1 ]x1 + [1] >= [-& 1 ]x1 + [1] = c(a(c(a(x1))))
         
                       [-& 0 ]     [1]    [-& 0 ]     [0]        
         c(b(c(x1))) = [1  -&]x1 + [1] >= [1  -&]x1 + [1] = b(x1)
        problem:
         DPs:
          
         TRS:
          a(x1) -> b(x1)
          a(b(x1)) -> c(a(c(a(x1))))
          c(b(c(x1))) -> b(x1)
        Qed