YES

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

Proof:
 DP Processor:
  DPs:
   a#(x1) -> b#(x1)
   a#(x1) -> b#(b(x1))
   b#(b(c(x1))) -> a#(x1)
   b#(b(c(x1))) -> c#(a(x1))
   b#(b(c(x1))) -> b#(c(a(x1)))
   b#(b(c(x1))) -> c#(b(c(a(x1))))
  TRS:
   a(x1) -> b(b(x1))
   b(b(c(x1))) -> c(b(c(a(x1))))
   c(c(x1)) -> x1
  TDG Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(x1) -> b#(b(x1))
    b#(b(c(x1))) -> a#(x1)
    b#(b(c(x1))) -> c#(a(x1))
    b#(b(c(x1))) -> b#(c(a(x1)))
    b#(b(c(x1))) -> c#(b(c(a(x1))))
   TRS:
    a(x1) -> b(b(x1))
    b(b(c(x1))) -> c(b(c(a(x1))))
    c(c(x1)) -> x1
   graph:
    b#(b(c(x1))) -> b#(c(a(x1))) -> b#(b(c(x1))) -> c#(b(c(a(x1))))
    b#(b(c(x1))) -> b#(c(a(x1))) -> b#(b(c(x1))) -> b#(c(a(x1)))
    b#(b(c(x1))) -> b#(c(a(x1))) -> b#(b(c(x1))) -> c#(a(x1))
    b#(b(c(x1))) -> b#(c(a(x1))) -> b#(b(c(x1))) -> a#(x1)
    b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(b(x1))
    b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
    a#(x1) -> b#(b(x1)) -> b#(b(c(x1))) -> c#(b(c(a(x1))))
    a#(x1) -> b#(b(x1)) -> b#(b(c(x1))) -> b#(c(a(x1)))
    a#(x1) -> b#(b(x1)) -> b#(b(c(x1))) -> c#(a(x1))
    a#(x1) -> b#(b(x1)) -> b#(b(c(x1))) -> a#(x1)
    a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(b(c(a(x1))))
    a#(x1) -> b#(x1) -> b#(b(c(x1))) -> b#(c(a(x1)))
    a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(a(x1))
    a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 14/36
    DPs:
     b#(b(c(x1))) -> b#(c(a(x1)))
     b#(b(c(x1))) -> a#(x1)
     a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1))
    TRS:
     a(x1) -> b(b(x1))
     b(b(c(x1))) -> c(b(c(a(x1))))
     c(c(x1)) -> x1
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
      [b#](x0) = [1 0]x0 + [0],
      
      [a#](x0) = [1 3]x0 + [2],
      
                [-& 0 ]     [1]
      [c](x0) = [0  2 ]x0 + [3],
      
                [-& 0 ]     [0]
      [b](x0) = [0  -&]x0 + [0],
      
                [0  0 ]     [0]
      [a](x0) = [-& 0 ]x0 + [0]
     orientation:
      b#(b(c(x1))) = [1 3]x1 + [4] >= [0 2]x1 + [3] = b#(c(a(x1)))
      
      b#(b(c(x1))) = [1 3]x1 + [4] >= [1 3]x1 + [2] = a#(x1)
      
      a#(x1) = [1 3]x1 + [2] >= [1 0]x1 + [0] = b#(x1)
      
      a#(x1) = [1 3]x1 + [2] >= [0 1]x1 + [1] = b#(b(x1))
      
              [0  0 ]     [0]         [0]           
      a(x1) = [-& 0 ]x1 + [0] >= x1 + [0] = b(b(x1))
      
                    [-& 0 ]     [1]    [-& 0 ]     [1]                 
      b(b(c(x1))) = [0  2 ]x1 + [3] >= [0  2 ]x1 + [3] = c(b(c(a(x1))))
      
                 [0 2]     [3]           
      c(c(x1)) = [2 4]x1 + [5] >= x1 = x1
     problem:
      DPs:
       b#(b(c(x1))) -> a#(x1)
       a#(x1) -> b#(x1)
      TRS:
       a(x1) -> b(b(x1))
       b(b(c(x1))) -> c(b(c(a(x1))))
       c(c(x1)) -> x1
     EDG Processor:
      DPs:
       b#(b(c(x1))) -> a#(x1)
       a#(x1) -> b#(x1)
      TRS:
       a(x1) -> b(b(x1))
       b(b(c(x1))) -> c(b(c(a(x1))))
       c(c(x1)) -> x1
      graph:
       b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
       a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1)
      CDG Processor:
       DPs:
        b#(b(c(x1))) -> a#(x1)
        a#(x1) -> b#(x1)
       TRS:
        a(x1) -> b(b(x1))
        b(b(c(x1))) -> c(b(c(a(x1))))
        c(c(x1)) -> x1
       graph:
        b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 1/4