YES

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

Proof:
 DP Processor:
  DPs:
   c#(c(c(c(x1)))) -> b#(x1)
   c#(c(c(c(x1)))) -> b#(b(x1))
   c#(c(c(c(x1)))) -> b#(b(b(x1)))
   c#(c(c(c(x1)))) -> b#(b(b(b(x1))))
   b#(b(x1)) -> c#(x1)
   b#(b(x1)) -> b#(c(x1))
   b#(b(x1)) -> c#(b(c(x1)))
  TRS:
   c(c(c(c(x1)))) -> b(b(b(b(x1))))
   b(b(x1)) -> x1
   b(b(x1)) -> c(b(c(x1)))
  TDG Processor:
   DPs:
    c#(c(c(c(x1)))) -> b#(x1)
    c#(c(c(c(x1)))) -> b#(b(x1))
    c#(c(c(c(x1)))) -> b#(b(b(x1)))
    c#(c(c(c(x1)))) -> b#(b(b(b(x1))))
    b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> b#(c(x1))
    b#(b(x1)) -> c#(b(c(x1)))
   TRS:
    c(c(c(c(x1)))) -> b(b(b(b(x1))))
    b(b(x1)) -> x1
    b(b(x1)) -> c(b(c(x1)))
   graph:
    b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> c#(b(c(x1)))
    b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> b#(c(x1))
    b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> c#(b(c(x1))) -> c#(c(c(c(x1)))) -> b#(b(b(b(x1))))
    b#(b(x1)) -> c#(b(c(x1))) -> c#(c(c(c(x1)))) -> b#(b(b(x1)))
    b#(b(x1)) -> c#(b(c(x1))) -> c#(c(c(c(x1)))) -> b#(b(x1))
    b#(b(x1)) -> c#(b(c(x1))) -> c#(c(c(c(x1)))) -> b#(x1)
    b#(b(x1)) -> c#(x1) -> c#(c(c(c(x1)))) -> b#(b(b(b(x1))))
    b#(b(x1)) -> c#(x1) -> c#(c(c(c(x1)))) -> b#(b(b(x1)))
    b#(b(x1)) -> c#(x1) -> c#(c(c(c(x1)))) -> b#(b(x1))
    b#(b(x1)) -> c#(x1) -> c#(c(c(c(x1)))) -> b#(x1)
    c#(c(c(c(x1)))) -> b#(b(b(b(x1)))) ->
    b#(b(x1)) -> c#(b(c(x1)))
    c#(c(c(c(x1)))) -> b#(b(b(b(x1)))) -> b#(b(x1)) -> b#(c(x1))
    c#(c(c(c(x1)))) -> b#(b(b(b(x1)))) -> b#(b(x1)) -> c#(x1)
    c#(c(c(c(x1)))) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(b(c(x1)))
    c#(c(c(c(x1)))) -> b#(b(b(x1))) -> b#(b(x1)) -> b#(c(x1))
    c#(c(c(c(x1)))) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(x1)
    c#(c(c(c(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> c#(b(c(x1)))
    c#(c(c(c(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> b#(c(x1))
    c#(c(c(c(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> c#(x1)
    c#(c(c(c(x1)))) -> b#(x1) -> b#(b(x1)) -> c#(b(c(x1)))
    c#(c(c(c(x1)))) -> b#(x1) -> b#(b(x1)) -> b#(c(x1))
    c#(c(c(c(x1)))) -> b#(x1) -> b#(b(x1)) -> c#(x1)
   Arctic Interpretation Processor:
    dimension: 2
    interpretation:
     [b#](x0) = [3 0]x0 + [0],
     
     [c#](x0) = [0 0]x0 + [-4],
     
               [0  -2]     [1]
     [b](x0) = [2  -3]x0 + [1],
     
               [-4 -3]     [0]
     [c](x0) = [1  1 ]x0 + [3]
    orientation:
     c#(c(c(c(x1)))) = [3 3]x1 + [5] >= [3 0]x1 + [0] = b#(x1)
     
     c#(c(c(c(x1)))) = [3 3]x1 + [5] >= [3 1]x1 + [4] = b#(b(x1))
     
     c#(c(c(c(x1)))) = [3 3]x1 + [5] >= [3 1]x1 + [4] = b#(b(b(x1)))
     
     c#(c(c(c(x1)))) = [3 3]x1 + [5] >= [3 1]x1 + [4] = b#(b(b(b(x1))))
     
     b#(b(x1)) = [3 1]x1 + [4] >= [0 0]x1 + [-4] = c#(x1)
     
     b#(b(x1)) = [3 1]x1 + [4] >= [1 1]x1 + [3] = b#(c(x1))
     
     b#(b(x1)) = [3 1]x1 + [4] >= [-1 -1]x1 + [2] = c#(b(c(x1)))
     
                      [0 0]     [2]    [0  -2]     [1]                 
     c(c(c(c(x1)))) = [4 4]x1 + [6] >= [2  0 ]x1 + [3] = b(b(b(b(x1))))
     
                [0  -2]     [1]           
     b(b(x1)) = [2  0 ]x1 + [3] >= x1 = x1
     
                [0  -2]     [1]    [-5 -4]     [0]              
     b(b(x1)) = [2  0 ]x1 + [3] >= [0  0 ]x1 + [3] = c(b(c(x1)))
    problem:
     DPs:
      c#(c(c(c(x1)))) -> b#(x1)
      c#(c(c(c(x1)))) -> b#(b(x1))
      c#(c(c(c(x1)))) -> b#(b(b(x1)))
      c#(c(c(c(x1)))) -> b#(b(b(b(x1))))
      b#(b(x1)) -> b#(c(x1))
     TRS:
      c(c(c(c(x1)))) -> b(b(b(b(x1))))
      b(b(x1)) -> x1
      b(b(x1)) -> c(b(c(x1)))
    EDG Processor:
     DPs:
      c#(c(c(c(x1)))) -> b#(x1)
      c#(c(c(c(x1)))) -> b#(b(x1))
      c#(c(c(c(x1)))) -> b#(b(b(x1)))
      c#(c(c(c(x1)))) -> b#(b(b(b(x1))))
      b#(b(x1)) -> b#(c(x1))
     TRS:
      c(c(c(c(x1)))) -> b(b(b(b(x1))))
      b(b(x1)) -> x1
      b(b(x1)) -> c(b(c(x1)))
     graph:
      b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> b#(c(x1))
      c#(c(c(c(x1)))) -> b#(b(b(b(x1)))) -> b#(b(x1)) -> b#(c(x1))
      c#(c(c(c(x1)))) -> b#(b(b(x1))) -> b#(b(x1)) -> b#(c(x1))
      c#(c(c(c(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> b#(c(x1))
      c#(c(c(c(x1)))) -> b#(x1) -> b#(b(x1)) -> b#(c(x1))
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 5/25
      DPs:
       b#(b(x1)) -> b#(c(x1))
      TRS:
       c(c(c(c(x1)))) -> b(b(b(b(x1))))
       b(b(x1)) -> x1
       b(b(x1)) -> c(b(c(x1)))
      Arctic Interpretation Processor:
       dimension: 2
       interpretation:
        [b#](x0) = [-4 2 ]x0 + [0],
        
                  [-2 2 ]     [1]
        [b](x0) = [-2 0 ]x0 + [0],
        
                  [1  1 ]     [2 ]
        [c](x0) = [-3 -&]x0 + [-&]
       orientation:
        b#(b(x1)) = [0 2]x1 + [2] >= [-1 -3]x1 + [0] = b#(c(x1))
        
                         [4 4]     [5]    [0  2 ]     [2]                 
        c(c(c(c(x1)))) = [0 0]x1 + [1] >= [-2 0 ]x1 + [0] = b(b(b(b(x1))))
        
                   [0  2 ]     [2]           
        b(b(x1)) = [-2 0 ]x1 + [0] >= x1 = x1
        
                   [0  2 ]     [2]    [0  0 ]     [2 ]              
        b(b(x1)) = [-2 0 ]x1 + [0] >= [-4 -4]x1 + [-2] = c(b(c(x1)))
       problem:
        DPs:
         
        TRS:
         c(c(c(c(x1)))) -> b(b(b(b(x1))))
         b(b(x1)) -> x1
         b(b(x1)) -> c(b(c(x1)))
       Qed