YES

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

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