YES

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

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