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:
                 [-& 0 ]     [1 ]
       [b](x0) = [0  -2]x0 + [-&],
       
       [a#](x0) = [-& 0 ]x0 + [0],
       
                 [-& 0 ]     [1 ]
       [a](x0) = [0  2 ]x0 + [-&],
       
                 [0  0 ]  
       [c](x0) = [0  -&]x0
      orientation:
       a#(a(b(x1))) = [2 0]x1 + [1] >= [0  -&]x1 + [0] = a#(c(x1))
       
       a#(a(b(x1))) = [2 0]x1 + [1] >= [2 0]x1 + [0] = a#(a(c(x1)))
       
               [-& 0 ]     [1 ]    [-& 0 ]     [1 ]        
       a(x1) = [0  2 ]x1 + [-&] >= [0  -2]x1 + [-&] = b(x1)
       
                     [2 0]     [1]    [2 0]     [1]                    
       a(a(b(x1))) = [4 2]x1 + [3] >= [4 2]x1 + [3] = a(b(a(a(c(x1)))))
       
                  [0  0 ]     [1]           
       c(b(x1)) = [-& 0 ]x1 + [1] >= 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:
                    [0 0]     [0]
          [b](x0) = [1 0]x0 + [0],
          
          [a#](x0) = [-& 0 ]x0 + [0],
          
                    [0 0]     [0]
          [a](x0) = [1 1]x0 + [0],
          
                    [0  -&]  
          [c](x0) = [0  -&]x0
         orientation:
          a#(a(b(x1))) = [2 1]x1 + [1] >= [1  -&]x1 + [0] = a#(a(c(x1)))
          
                  [0 0]     [0]    [0 0]     [0]        
          a(x1) = [1 1]x1 + [0] >= [1 0]x1 + [0] = b(x1)
          
                        [2 1]     [1]    [2  -&]     [1]                    
          a(a(b(x1))) = [3 2]x1 + [2] >= [3  -&]x1 + [2] = a(b(a(a(c(x1)))))
          
                     [0 0]     [0]           
          c(b(x1)) = [0 0]x1 + [0] >= x1 = x1
         problem:
          DPs:
           
          TRS:
           a(x1) -> b(x1)
           a(a(b(x1))) -> a(b(a(a(c(x1)))))
           c(b(x1)) -> x1
         Qed