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: 2
     usable rules:
      a(x1) -> b(x1)
      a(a(c(x1))) -> c(a(c(a(a(x1)))))
      c(c(x1)) -> x1
     interpretation:
                [0 ]
      [b](x0) = [-&],
      
      [a#](x0) = [0 1]x0 + [0],
      
                [-& 0 ]     [0]
      [a](x0) = [0  -&]x0 + [0],
      
                [1  0 ]     [1]
      [c](x0) = [0  -&]x0 + [0]
     orientation:
      a#(a(c(x1))) = [2 1]x1 + [2] >= [1 0]x1 + [1] = a#(c(a(a(x1))))
      
      a#(a(c(x1))) = [2 1]x1 + [2] >= [0 1]x1 + [0] = a#(x1)
      
      a#(a(c(x1))) = [2 1]x1 + [2] >= [1 0]x1 + [1] = a#(a(x1))
      
              [-& 0 ]     [0]    [0 ]        
      a(x1) = [0  -&]x1 + [0] >= [-&] = b(x1)
      
                    [1  0 ]     [1]    [1  0 ]     [1]                    
      a(a(c(x1))) = [0  -&]x1 + [0] >= [0  -&]x1 + [0] = c(a(c(a(a(x1)))))
      
                 [2 1]     [2]           
      c(c(x1)) = [1 0]x1 + [1] >= x1 = x1
     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
     Restore Modifier:
      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)
       Usable Rule Processor:
        DPs:
         a#(a(c(x1))) -> a#(x1)
        TRS:
         
        Arctic Interpretation Processor:
         dimension: 1
         usable rules:
          
         interpretation:
          [a#](x0) = x0,
          
          [a](x0) = x0 + 0,
          
          [c](x0) = 1x0 + 13
         orientation:
          a#(a(c(x1))) = 1x1 + 13 >= x1 = a#(x1)
         problem:
          DPs:
           
          TRS:
           
         Qed