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
     interpretation:
      [a#](x0) = [-& 0  0  0 ]x0 + [0],
      
                [0  0  0  0 ]     [0 ]
                [-& 0  0  -&]     [-&]
      [c](x0) = [0  0  0  0 ]x0 + [1 ]
                [0  0  0  0 ]     [1 ],
      
                [0  1  0  0 ]     [-&]
                [-& 0  -& -&]     [-&]
      [b](x0) = [-& 0  -& -&]x0 + [0 ]
                [-& 0  0  -&]     [0 ],
      
                [0  0  0  0 ]     [0]
                [-& 0  -& -&]     [0]
      [a](x0) = [-& 0  0  0 ]x0 + [0]
                [0  0  0  0 ]     [1]
     orientation:
      a#(a(b(x1))) = [0 1 0 0]x1 + [1] >= [-& 0  -& -&]x1 + [0] = a#(b(b(a(a(x1)))))
      
      a#(a(b(x1))) = [0 1 0 0]x1 + [1] >= [-& 0  0  0 ]x1 + [0] = a#(x1)
      
      a#(a(b(x1))) = [0 1 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = a#(a(x1))
      
              [0  0  0  0 ]     [0]           
              [-& 0  -& -&]     [0]           
      a(x1) = [-& 0  0  0 ]x1 + [0] >= x1 = x1
              [0  0  0  0 ]     [1]           
      
                    [0  1  0  0 ]     [1]    [0  1  0  0 ]     [1]                       
                    [-& 0  -& -&]     [0]    [-& 0  -& -&]     [0]                       
      a(a(b(x1))) = [0  1  0  0 ]x1 + [1] >= [0  1  0  0 ]x1 + [1] = c(a(b(b(a(a(x1))))))
                    [0  1  0  0 ]     [1]    [0  1  0  0 ]     [1]                       
      
                 [0  1  1  0 ]     [1 ]           
                 [-& 0  0  -&]     [-&]           
      b(c(x1)) = [-& 0  0  -&]x1 + [0 ] >= x1 = x1
                 [0  0  0  0 ]     [1 ]           
     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
     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: 1
       interpretation:
        [a#](x0) = -1x0 + 0,
        
        [c](x0) = -1x0 + 0,
        
        [b](x0) = 1x0 + 8,
        
        [a](x0) = x0 + 1
       orientation:
        a#(a(b(x1))) = x1 + 7 >= -1x1 + 0 = a#(x1)
        
        a#(a(b(x1))) = x1 + 7 >= -1x1 + 0 = a#(a(x1))
        
        a(x1) = x1 + 1 >= x1 = x1
        
        a(a(b(x1))) = 1x1 + 8 >= 1x1 + 8 = c(a(b(b(a(a(x1))))))
        
        b(c(x1)) = x1 + 8 >= x1 = x1
       problem:
        DPs:
         
        TRS:
         a(x1) -> x1
         a(a(b(x1))) -> c(a(b(b(a(a(x1))))))
         b(c(x1)) -> x1
       Qed