YES

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

Proof:
 DP Processor:
  DPs:
   a#(x1) -> b#(x1)
   b#(b(c(x1))) -> b#(x1)
   b#(b(c(x1))) -> a#(b(x1))
   b#(b(c(x1))) -> c#(a(b(x1)))
   b#(b(c(x1))) -> a#(c(a(b(x1))))
   b#(b(c(x1))) -> c#(a(c(a(b(x1)))))
  TRS:
   a(x1) -> b(x1)
   b(b(c(x1))) -> c(a(c(a(b(x1)))))
   c(c(x1)) -> x1
  TDG Processor:
   DPs:
    a#(x1) -> b#(x1)
    b#(b(c(x1))) -> b#(x1)
    b#(b(c(x1))) -> a#(b(x1))
    b#(b(c(x1))) -> c#(a(b(x1)))
    b#(b(c(x1))) -> a#(c(a(b(x1))))
    b#(b(c(x1))) -> c#(a(c(a(b(x1)))))
   TRS:
    a(x1) -> b(x1)
    b(b(c(x1))) -> c(a(c(a(b(x1)))))
    c(c(x1)) -> x1
   graph:
    b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> c#(a(c(a(b(x1)))))
    b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> a#(c(a(b(x1))))
    b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> c#(a(b(x1)))
    b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> a#(b(x1))
    b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> b#(x1)
    b#(b(c(x1))) -> a#(c(a(b(x1)))) -> a#(x1) -> b#(x1)
    b#(b(c(x1))) -> a#(b(x1)) -> a#(x1) -> b#(x1)
    a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(a(c(a(b(x1)))))
    a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(c(a(b(x1))))
    a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(a(b(x1)))
    a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(b(x1))
    a#(x1) -> b#(x1) -> b#(b(c(x1))) -> b#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 12/36
    DPs:
     b#(b(c(x1))) -> b#(x1)
     b#(b(c(x1))) -> a#(b(x1))
     a#(x1) -> b#(x1)
     b#(b(c(x1))) -> a#(c(a(b(x1))))
    TRS:
     a(x1) -> b(x1)
     b(b(c(x1))) -> c(a(c(a(b(x1)))))
     c(c(x1)) -> x1
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> b(x1)
      b(b(c(x1))) -> c(a(c(a(b(x1)))))
      c(c(x1)) -> x1
     interpretation:
      [b#](x0) = [-& 0 ]x0 + [0],
      
      [a#](x0) = [-& 0 ]x0 + [0],
      
                [1  0 ]     [2]
      [c](x0) = [0  -&]x0 + [1],
      
                [-& 0 ]     [0]
      [b](x0) = [0  -&]x0 + [0],
      
                [-& 0 ]     [0]
      [a](x0) = [0  0 ]x0 + [2]
     orientation:
      b#(b(c(x1))) = [1 0]x1 + [2] >= [-& 0 ]x1 + [0] = b#(x1)
      
      b#(b(c(x1))) = [1 0]x1 + [2] >= [0  -&]x1 + [0] = a#(b(x1))
      
      a#(x1) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = b#(x1)
      
      b#(b(c(x1))) = [1 0]x1 + [2] >= [0  -&]x1 + [1] = a#(c(a(b(x1))))
      
              [-& 0 ]     [0]    [-& 0 ]     [0]        
      a(x1) = [0  0 ]x1 + [2] >= [0  -&]x1 + [0] = b(x1)
      
                    [1  0 ]     [2]    [1  0 ]     [2]                    
      b(b(c(x1))) = [0  -&]x1 + [1] >= [0  -&]x1 + [1] = c(a(c(a(b(x1)))))
      
                 [2 1]     [3]           
      c(c(x1)) = [1 0]x1 + [2] >= x1 = x1
     problem:
      DPs:
       b#(b(c(x1))) -> b#(x1)
       a#(x1) -> b#(x1)
      TRS:
       a(x1) -> b(x1)
       b(b(c(x1))) -> c(a(c(a(b(x1)))))
       c(c(x1)) -> x1
     Restore Modifier:
      DPs:
       b#(b(c(x1))) -> b#(x1)
       a#(x1) -> b#(x1)
      TRS:
       a(x1) -> b(x1)
       b(b(c(x1))) -> c(a(c(a(b(x1)))))
       c(c(x1)) -> x1
      EDG Processor:
       DPs:
        b#(b(c(x1))) -> b#(x1)
        a#(x1) -> b#(x1)
       TRS:
        a(x1) -> b(x1)
        b(b(c(x1))) -> c(a(c(a(b(x1)))))
        c(c(x1)) -> x1
       graph:
        b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> b#(x1)
        a#(x1) -> b#(x1) -> b#(b(c(x1))) -> b#(x1)
       CDG Processor:
        DPs:
         b#(b(c(x1))) -> b#(x1)
         a#(x1) -> b#(x1)
        TRS:
         a(x1) -> b(x1)
         b(b(c(x1))) -> c(a(c(a(b(x1)))))
         c(c(x1)) -> x1
        graph:
         
        Qed