YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> c#(a(x1))
   a#(a(b(x1))) -> a#(b(c(a(x1))))
   c#(b(x1)) -> a#(x1)
  TRS:
   a(x1) -> x1
   a(a(b(x1))) -> b(a(b(c(a(x1)))))
   c(b(x1)) -> a(x1)
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> c#(a(x1))
    a#(a(b(x1))) -> a#(b(c(a(x1))))
    c#(b(x1)) -> a#(x1)
   TRS:
    a(x1) -> x1
    a(a(b(x1))) -> b(a(b(c(a(x1)))))
    c(b(x1)) -> a(x1)
   graph:
    c#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(b(c(a(x1))))
    c#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> c#(a(x1))
    c#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> c#(a(x1)) -> c#(b(x1)) -> a#(x1)
    a#(a(b(x1))) -> a#(b(c(a(x1)))) ->
    a#(a(b(x1))) -> a#(b(c(a(x1))))
    a#(a(b(x1))) -> a#(b(c(a(x1)))) -> a#(a(b(x1))) -> c#(a(x1))
    a#(a(b(x1))) -> a#(b(c(a(x1)))) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(b(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#(b(c(a(x1))))
     c#(b(x1)) -> a#(x1)
    TRS:
     a(x1) -> x1
     a(a(b(x1))) -> b(a(b(c(a(x1)))))
     c(b(x1)) -> a(x1)
    graph:
     c#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
     c#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> c#(a(x1))
     c#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(b(c(a(x1))))
     a#(a(b(x1))) -> c#(a(x1)) -> c#(b(x1)) -> 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#(b(c(a(x1))))
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 7/16
     DPs:
      c#(b(x1)) -> a#(x1)
      a#(a(b(x1))) -> c#(a(x1))
      a#(a(b(x1))) -> a#(x1)
     TRS:
      a(x1) -> x1
      a(a(b(x1))) -> b(a(b(c(a(x1)))))
      c(b(x1)) -> a(x1)
     Arctic Interpretation Processor:
      dimension: 4
      interpretation:
       [c#](x0) = [0  -& 0  0 ]x0 + [0],
       
       [a#](x0) = [-& -& 0  0 ]x0 + [0],
       
                 [0  0  -& -&]     [0]
                 [0  0  -& 0 ]     [0]
       [c](x0) = [0  0  -& 0 ]x0 + [0]
                 [0  0  -& 0 ]     [0],
       
                 [0  0  0  0 ]     [0]
                 [1  0  0  0 ]     [1]
       [b](x0) = [0  0  0  0 ]x0 + [0]
                 [0  -& -& -&]     [0],
       
                 [0  -& 0  -&]     [-&]
                 [0  0  0  -&]     [0 ]
       [a](x0) = [1  0  0  0 ]x0 + [0 ]
                 [0  0  -& 0 ]     [0 ]
      orientation:
       c#(b(x1)) = [0 0 0 0]x1 + [0] >= [-& -& 0  0 ]x1 + [0] = a#(x1)
       
       a#(a(b(x1))) = [1 1 1 1]x1 + [1] >= [1 0 0 0]x1 + [0] = c#(a(x1))
       
       a#(a(b(x1))) = [1 1 1 1]x1 + [1] >= [-& -& 0  0 ]x1 + [0] = a#(x1)
       
               [0  -& 0  -&]     [-&]           
               [0  0  0  -&]     [0 ]           
       a(x1) = [1  0  0  0 ]x1 + [0 ] >= x1 = x1
               [0  0  -& 0 ]     [0 ]           
       
                     [1 1 1 1]     [1]    [1 1 1 1]     [1]                    
                     [1 1 1 1]     [1]    [1 1 1 1]     [1]                    
       a(a(b(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [1] = b(a(b(c(a(x1)))))
                     [1 0 0 0]     [1]    [0 0 0 0]     [0]                    
       
                  [1 0 0 0]     [1]    [0  -& 0  -&]     [-&]        
                  [1 0 0 0]     [1]    [0  0  0  -&]     [0 ]        
       c(b(x1)) = [1 0 0 0]x1 + [1] >= [1  0  0  0 ]x1 + [0 ] = a(x1)
                  [1 0 0 0]     [1]    [0  0  -& 0 ]     [0 ]        
      problem:
       DPs:
        c#(b(x1)) -> a#(x1)
        a#(a(b(x1))) -> c#(a(x1))
       TRS:
        a(x1) -> x1
        a(a(b(x1))) -> b(a(b(c(a(x1)))))
        c(b(x1)) -> a(x1)
      EDG Processor:
       DPs:
        c#(b(x1)) -> a#(x1)
        a#(a(b(x1))) -> c#(a(x1))
       TRS:
        a(x1) -> x1
        a(a(b(x1))) -> b(a(b(c(a(x1)))))
        c(b(x1)) -> a(x1)
       graph:
        c#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> c#(a(x1))
        a#(a(b(x1))) -> c#(a(x1)) -> c#(b(x1)) -> a#(x1)
       Arctic Interpretation Processor:
        dimension: 3
        interpretation:
         [c#](x0) = [0 0 1]x0 + [0],
         
         [a#](x0) = [0  -& -&]x0,
         
                   [-& 0  0 ]     [0]
         [c](x0) = [-& 0  0 ]x0 + [0]
                   [-& 0  0 ]     [0],
         
                   [0 0 0]     [-&]
         [b](x0) = [0 0 1]x0 + [0 ]
                   [0 0 0]     [1 ],
         
                   [0  0  1 ]     [0]
         [a](x0) = [0  0  0 ]x0 + [0]
                   [0  -& 0 ]     [1]
        orientation:
         c#(b(x1)) = [1 1 1]x1 + [2] >= [0  -& -&]x1 = a#(x1)
         
         a#(a(b(x1))) = [1 1 1]x1 + [2] >= [1 0 1]x1 + [2] = c#(a(x1))
         
                 [0  0  1 ]     [0]           
         a(x1) = [0  0  0 ]x1 + [0] >= x1 = x1
                 [0  -& 0 ]     [1]           
         
                       [1 1 1]     [2]    [1 1 1]     [2]                    
         a(a(b(x1))) = [1 1 1]x1 + [2] >= [1 1 1]x1 + [2] = b(a(b(c(a(x1)))))
                       [1 1 1]     [2]    [1 1 1]     [2]                    
         
                    [0 0 1]     [1]    [0  0  1 ]     [0]        
         c(b(x1)) = [0 0 1]x1 + [1] >= [0  0  0 ]x1 + [0] = a(x1)
                    [0 0 1]     [1]    [0  -& 0 ]     [1]        
        problem:
         DPs:
          a#(a(b(x1))) -> c#(a(x1))
         TRS:
          a(x1) -> x1
          a(a(b(x1))) -> b(a(b(c(a(x1)))))
          c(b(x1)) -> a(x1)
        EDG Processor:
         DPs:
          a#(a(b(x1))) -> c#(a(x1))
         TRS:
          a(x1) -> x1
          a(a(b(x1))) -> b(a(b(c(a(x1)))))
          c(b(x1)) -> a(x1)
         graph:
          
         Qed