YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> c#(x1)
   a#(a(b(x1))) -> a#(c(x1))
   a#(a(b(x1))) -> a#(a(c(x1)))
   a#(a(b(x1))) -> a#(b(a(a(c(x1)))))
  TRS:
   a(x1) -> b(x1)
   a(a(b(x1))) -> a(b(a(a(c(x1)))))
   c(b(x1)) -> x1
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> c#(x1)
    a#(a(b(x1))) -> a#(c(x1))
    a#(a(b(x1))) -> a#(a(c(x1)))
    a#(a(b(x1))) -> a#(b(a(a(c(x1)))))
   TRS:
    a(x1) -> b(x1)
    a(a(b(x1))) -> a(b(a(a(c(x1)))))
    c(b(x1)) -> x1
   graph:
    a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> a#(b(a(a(c(x1)))))
    a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> a#(a(c(x1)))
    a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> a#(c(x1))
    a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> c#(x1)
    a#(a(b(x1))) -> a#(b(a(a(c(x1))))) ->
    a#(a(b(x1))) -> a#(b(a(a(c(x1)))))
    a#(a(b(x1))) -> a#(b(a(a(c(x1))))) ->
    a#(a(b(x1))) -> a#(a(c(x1)))
    a#(a(b(x1))) -> a#(b(a(a(c(x1))))) ->
    a#(a(b(x1))) -> a#(c(x1))
    a#(a(b(x1))) -> a#(b(a(a(c(x1))))) -> a#(a(b(x1))) -> c#(x1)
    a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> a#(b(a(a(c(x1)))))
    a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> a#(a(c(x1)))
    a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> a#(c(x1))
    a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> c#(x1)
   EDG Processor:
    DPs:
     a#(a(b(x1))) -> c#(x1)
     a#(a(b(x1))) -> a#(c(x1))
     a#(a(b(x1))) -> a#(a(c(x1)))
     a#(a(b(x1))) -> a#(b(a(a(c(x1)))))
    TRS:
     a(x1) -> b(x1)
     a(a(b(x1))) -> a(b(a(a(c(x1)))))
     c(b(x1)) -> x1
    graph:
     a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> c#(x1)
     a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> a#(c(x1))
     a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> a#(a(c(x1)))
     a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> a#(b(a(a(c(x1)))))
     a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> c#(x1)
     a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> a#(c(x1))
     a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> a#(a(c(x1)))
     a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> a#(b(a(a(c(x1)))))
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 8/16
     DPs:
      a#(a(b(x1))) -> a#(c(x1))
      a#(a(b(x1))) -> a#(a(c(x1)))
     TRS:
      a(x1) -> b(x1)
      a(a(b(x1))) -> a(b(a(a(c(x1)))))
      c(b(x1)) -> x1
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> b(x1)
       a(a(b(x1))) -> a(b(a(a(c(x1)))))
       c(b(x1)) -> x1
      interpretation:
       [a#](x0) = [-& 0 ]x0 + [0],
       
                 [-& 0 ]     [1]
       [c](x0) = [0  -&]x0 + [1],
       
                 [-& 0 ]     [2]
       [b](x0) = [0  -&]x0 + [1],
       
                 [-& 0 ]     [2]
       [a](x0) = [0  3 ]x0 + [2]
      orientation:
       a#(a(b(x1))) = [3 0]x1 + [4] >= [0  -&]x1 + [1] = a#(c(x1))
       
       a#(a(b(x1))) = [3 0]x1 + [4] >= [3 0]x1 + [4] = a#(a(c(x1)))
       
               [-& 0 ]     [2]    [-& 0 ]     [2]        
       a(x1) = [0  3 ]x1 + [2] >= [0  -&]x1 + [1] = b(x1)
       
                     [3 0]     [4]    [3 0]     [4]                    
       a(a(b(x1))) = [6 3]x1 + [7] >= [6 3]x1 + [7] = a(b(a(a(c(x1)))))
       
                       [1]           
       c(b(x1)) = x1 + [2] >= x1 = x1
      problem:
       DPs:
        a#(a(b(x1))) -> a#(a(c(x1)))
       TRS:
        a(x1) -> b(x1)
        a(a(b(x1))) -> a(b(a(a(c(x1)))))
        c(b(x1)) -> x1
      Restore Modifier:
       DPs:
        a#(a(b(x1))) -> a#(a(c(x1)))
       TRS:
        a(x1) -> b(x1)
        a(a(b(x1))) -> a(b(a(a(c(x1)))))
        c(b(x1)) -> x1
       EDG Processor:
        DPs:
         a#(a(b(x1))) -> a#(a(c(x1)))
        TRS:
         a(x1) -> b(x1)
         a(a(b(x1))) -> a(b(a(a(c(x1)))))
         c(b(x1)) -> x1
        graph:
         a#(a(b(x1))) -> a#(a(c(x1))) -> a#(a(b(x1))) -> a#(a(c(x1)))
        Arctic Interpretation Processor:
         dimension: 2
         usable rules:
          a(x1) -> b(x1)
          a(a(b(x1))) -> a(b(a(a(c(x1)))))
          c(b(x1)) -> x1
         interpretation:
          [a#](x0) = [3 0]x0 + [0],
          
                    [-& 0 ]     [0]
          [c](x0) = [-& 0 ]x0 + [0],
          
                    [0 1]     [-&]
          [b](x0) = [0 0]x0 + [3 ],
          
                    [1 1]     [0]
          [a](x0) = [0 0]x0 + [3]
         orientation:
          a#(a(b(x1))) = [4 5]x1 + [7] >= [-& 4 ]x1 + [4] = a#(a(c(x1)))
          
                  [1 1]     [0]    [0 1]     [-&]        
          a(x1) = [0 0]x1 + [3] >= [0 0]x1 + [3 ] = b(x1)
          
                        [2 3]     [5]    [-& 3 ]     [5]                    
          a(a(b(x1))) = [1 2]x1 + [4] >= [-& 2 ]x1 + [4] = a(b(a(a(c(x1)))))
          
                     [0 0]     [3]           
          c(b(x1)) = [0 0]x1 + [3] >= x1 = x1
         problem:
          DPs:
           
          TRS:
           a(x1) -> b(x1)
           a(a(b(x1))) -> a(b(a(a(c(x1)))))
           c(b(x1)) -> x1
         Qed