YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> a#(a(x1))
   a#(a(b(x1))) -> b#(a(a(x1)))
   a#(a(b(x1))) -> b#(b(a(a(x1))))
   a#(a(b(x1))) -> a#(b(b(a(a(x1)))))
  TRS:
   a(x1) -> x1
   a(a(b(x1))) -> c(a(b(b(a(a(x1))))))
   b(c(x1)) -> x1
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> b#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(b(b(a(a(x1)))))
   TRS:
    a(x1) -> x1
    a(a(b(x1))) -> c(a(b(b(a(a(x1))))))
    b(c(x1)) -> x1
   graph:
    a#(a(b(x1))) -> a#(b(b(a(a(x1))))) ->
    a#(a(b(x1))) -> a#(b(b(a(a(x1)))))
    a#(a(b(x1))) -> a#(b(b(a(a(x1))))) ->
    a#(a(b(x1))) -> b#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(b(b(a(a(x1))))) ->
    a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(b(b(a(a(x1))))) ->
    a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(b(b(a(a(x1))))) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(b(b(a(a(x1)))))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(b(b(a(a(x1)))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 15/25
    DPs:
     a#(a(b(x1))) -> a#(b(b(a(a(x1)))))
     a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(a(x1))
    TRS:
     a(x1) -> x1
     a(a(b(x1))) -> c(a(b(b(a(a(x1))))))
     b(c(x1)) -> x1
    Arctic Interpretation Processor:
     dimension: 4
     usable rules:
      a(x1) -> x1
      a(a(b(x1))) -> c(a(b(b(a(a(x1))))))
      b(c(x1)) -> x1
     interpretation:
      [a#](x0) = [0  0  -& 0 ]x0 + [0],
      
                [0  0  0  0 ]     [0 ]
                [-& 0  0  0 ]     [-&]
      [c](x0) = [0  0  0  0 ]x0 + [-&]
                [0  -& -& 0 ]     [0 ],
      
                [-& -& -& 0 ]     [0 ]
                [0  -& -& 0 ]     [-&]
      [b](x0) = [0  0  0  1 ]x0 + [0 ]
                [-& -& -& 0 ]     [0 ],
      
                [0  0  -& 0 ]     [0]
                [0  0  0  0 ]     [1]
      [a](x0) = [0  0  0  0 ]x0 + [0]
                [-& -& -& 0 ]     [0]
     orientation:
      a#(a(b(x1))) = [0 0 0 1]x1 + [1] >= [-& -& -& 0 ]x1 + [0] = a#(b(b(a(a(x1)))))
      
      a#(a(b(x1))) = [0 0 0 1]x1 + [1] >= [0  0  -& 0 ]x1 + [0] = a#(x1)
      
      a#(a(b(x1))) = [0 0 0 1]x1 + [1] >= [0 0 0 0]x1 + [1] = a#(a(x1))
      
              [0  0  -& 0 ]     [0]           
              [0  0  0  0 ]     [1]           
      a(x1) = [0  0  0  0 ]x1 + [0] >= x1 = x1
              [-& -& -& 0 ]     [0]           
      
                    [0  0  0  1 ]     [1]    [0  0  0  1 ]     [1]                       
                    [0  0  0  1 ]     [1]    [0  0  0  1 ]     [1]                       
      a(a(b(x1))) = [0  0  0  1 ]x1 + [1] >= [0  0  0  1 ]x1 + [1] = c(a(b(b(a(a(x1))))))
                    [-& -& -& 0 ]     [0]    [-& -& -& 0 ]     [0]                       
      
                 [0  -& -& 0 ]     [0]           
                 [0  0  0  0 ]     [0]           
      b(c(x1)) = [1  0  0  1 ]x1 + [1] >= x1 = x1
                 [0  -& -& 0 ]     [0]           
     problem:
      DPs:
       a#(a(b(x1))) -> a#(x1)
       a#(a(b(x1))) -> a#(a(x1))
      TRS:
       a(x1) -> x1
       a(a(b(x1))) -> c(a(b(b(a(a(x1))))))
       b(c(x1)) -> x1
     Restore Modifier:
      DPs:
       a#(a(b(x1))) -> a#(x1)
       a#(a(b(x1))) -> a#(a(x1))
      TRS:
       a(x1) -> x1
       a(a(b(x1))) -> c(a(b(b(a(a(x1))))))
       b(c(x1)) -> x1
      EDG Processor:
       DPs:
        a#(a(b(x1))) -> a#(x1)
        a#(a(b(x1))) -> a#(a(x1))
       TRS:
        a(x1) -> x1
        a(a(b(x1))) -> c(a(b(b(a(a(x1))))))
        b(c(x1)) -> x1
       graph:
        a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
        a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
        a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
        a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
       Arctic Interpretation Processor:
        dimension: 2
        usable rules:
         a(x1) -> x1
         a(a(b(x1))) -> c(a(b(b(a(a(x1))))))
        interpretation:
         [a#](x0) = [0 1]x0 + [0],
         
                   [0 ]
         [c](x0) = [-&],
         
                   [0  -&]     [0 ]
         [b](x0) = [-& 2 ]x0 + [-&],
         
                   [1  -&]  
         [a](x0) = [0  1 ]x0
        orientation:
         a#(a(b(x1))) = [1 4]x1 + [1] >= [0 1]x1 + [0] = a#(x1)
         
         a#(a(b(x1))) = [1 4]x1 + [1] >= [1 2]x1 + [0] = a#(a(x1))
         
                 [1  -&]             
         a(x1) = [0  1 ]x1 >= x1 = x1
         
                       [2  -&]     [2]    [0 ]                       
         a(a(b(x1))) = [1  4 ]x1 + [1] >= [-&] = c(a(b(b(a(a(x1))))))
         
                    [0 ]           
         b(c(x1)) = [-&] >= x1 = x1
        problem:
         DPs:
          a#(a(b(x1))) -> a#(a(x1))
         TRS:
          a(x1) -> x1
          a(a(b(x1))) -> c(a(b(b(a(a(x1))))))
          b(c(x1)) -> x1
        Restore Modifier:
         DPs:
          a#(a(b(x1))) -> a#(a(x1))
         TRS:
          a(x1) -> x1
          a(a(b(x1))) -> c(a(b(b(a(a(x1))))))
          b(c(x1)) -> x1
         EDG Processor:
          DPs:
           a#(a(b(x1))) -> a#(a(x1))
          TRS:
           a(x1) -> x1
           a(a(b(x1))) -> c(a(b(b(a(a(x1))))))
           b(c(x1)) -> x1
          graph:
           a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
          Arctic Interpretation Processor:
           dimension: 3
           usable rules:
            a(x1) -> x1
            a(a(b(x1))) -> c(a(b(b(a(a(x1))))))
           interpretation:
            [a#](x0) = [-& 1  0 ]x0 + [0],
            
                      [0 ]
            [c](x0) = [-&]
                      [-&],
            
                      [-& 0  0 ]     [0]
            [b](x0) = [-& 0  0 ]x0 + [0]
                      [1  1  1 ]     [1],
            
                      [0 0 0]     [0]
            [a](x0) = [0 0 0]x0 + [0]
                      [0 0 0]     [1]
           orientation:
            a#(a(b(x1))) = [2 2 2]x1 + [2] >= [1 1 1]x1 + [1] = a#(a(x1))
            
                    [0 0 0]     [0]           
            a(x1) = [0 0 0]x1 + [0] >= x1 = x1
                    [0 0 0]     [1]           
            
                          [1 1 1]     [1]    [0 ]                       
            a(a(b(x1))) = [1 1 1]x1 + [1] >= [-&] = c(a(b(b(a(a(x1))))))
                          [1 1 1]     [1]    [-&]                       
            
                       [0]           
            b(c(x1)) = [0] >= x1 = x1
                       [1]           
           problem:
            DPs:
             
            TRS:
             a(x1) -> x1
             a(a(b(x1))) -> c(a(b(b(a(a(x1))))))
             b(c(x1)) -> x1
           Qed