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: 3
      usable rules:
       a(x1) -> x1
       a(a(b(x1))) -> b(a(b(c(a(x1)))))
       c(b(x1)) -> a(x1)
      interpretation:
       [c#](x0) = [1  -& 1 ]x0 + [0],
       
       [a#](x0) = [-& 0  1 ]x0 + [0],
       
                 [0  -& -&]     [-&]
       [c](x0) = [0  0  -&]x0 + [1 ]
                 [0  0  -&]     [0 ],
       
                 [0  0  0 ]     [1]
       [b](x0) = [1  0  0 ]x0 + [1]
                 [-& 0  0 ]     [1],
       
                 [0  -& 0 ]     [-&]
       [a](x0) = [0  0  0 ]x0 + [-&]
                 [1  0  0 ]     [0 ]
      orientation:
       c#(b(x1)) = [1 1 1]x1 + [2] >= [-& 0  1 ]x1 + [0] = a#(x1)
       
       a#(a(b(x1))) = [2 2 2]x1 + [3] >= [2 1 1]x1 + [1] = c#(a(x1))
       
       a#(a(b(x1))) = [2 2 2]x1 + [3] >= [-& 0  1 ]x1 + [0] = a#(x1)
       
               [0  -& 0 ]     [-&]           
       a(x1) = [0  0  0 ]x1 + [-&] >= x1 = x1
               [1  0  0 ]     [0 ]           
       
                     [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 0]     [1]    [0  -& 0 ]     [-&]        
       c(b(x1)) = [1 0 0]x1 + [1] >= [0  0  0 ]x1 + [-&] = a(x1)
                  [1 0 0]     [1]    [1  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)
      Restore Modifier:
       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: 4
         usable rules:
          a(x1) -> x1
          a(a(b(x1))) -> b(a(b(c(a(x1)))))
          c(b(x1)) -> a(x1)
         interpretation:
          [c#](x0) = [0  1  -& 1 ]x0 + [0],
          
          [a#](x0) = [0 0 0 0]x0,
          
                    [0  -& -& -&]     [0]
                    [0  -& -& -&]     [0]
          [c](x0) = [0  -& -& -&]x0 + [0]
                    [0  -& -& -&]     [0],
          
                    [0  0  0  1 ]     [0]
                    [0  0  0  0 ]     [0]
          [b](x0) = [0  0  0  0 ]x0 + [0]
                    [0  0  0  -&]     [0],
          
                    [0  0  0  -&]     [0]
                    [-& 0  0  0 ]     [0]
          [a](x0) = [-& 0  0  1 ]x0 + [0]
                    [-& 0  0  0 ]     [0]
         orientation:
          c#(b(x1)) = [1 1 1 1]x1 + [1] >= [0 0 0 0]x1 = a#(x1)
          
          a#(a(b(x1))) = [1 1 1 1]x1 + [1] >= [0 1 1 1]x1 + [1] = c#(a(x1))
          
                  [0  0  0  -&]     [0]           
                  [-& 0  0  0 ]     [0]           
          a(x1) = [-& 0  0  1 ]x1 + [0] >= x1 = x1
                  [-& 0  0  0 ]     [0]           
          
                        [1 1 1 1]     [1]    [1  1  1  -&]     [1]                    
                        [1 1 1 0]     [1]    [1  1  1  -&]     [1]                    
          a(a(b(x1))) = [1 1 1 1]x1 + [1] >= [1  1  1  -&]x1 + [1] = b(a(b(c(a(x1)))))
                        [1 1 1 0]     [1]    [1  1  1  -&]     [1]                    
          
                     [0 0 0 1]     [0]    [0  0  0  -&]     [0]        
                     [0 0 0 1]     [0]    [-& 0  0  0 ]     [0]        
          c(b(x1)) = [0 0 0 1]x1 + [0] >= [-& 0  0  1 ]x1 + [0] = a(x1)
                     [0 0 0 1]     [0]    [-& 0  0  0 ]     [0]        
         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)
         Restore Modifier:
          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