YES

Problem:
 c(c(b(c(x)))) -> b(a(0(),c(x)))
 c(c(x)) -> b(c(b(c(x))))
 a(0(),x) -> c(c(x))

Proof:
 DP Processor:
  DPs:
   c#(c(b(c(x)))) -> a#(0(),c(x))
   c#(c(x)) -> c#(b(c(x)))
   a#(0(),x) -> c#(x)
   a#(0(),x) -> c#(c(x))
  TRS:
   c(c(b(c(x)))) -> b(a(0(),c(x)))
   c(c(x)) -> b(c(b(c(x))))
   a(0(),x) -> c(c(x))
  TDG Processor:
   DPs:
    c#(c(b(c(x)))) -> a#(0(),c(x))
    c#(c(x)) -> c#(b(c(x)))
    a#(0(),x) -> c#(x)
    a#(0(),x) -> c#(c(x))
   TRS:
    c(c(b(c(x)))) -> b(a(0(),c(x)))
    c(c(x)) -> b(c(b(c(x))))
    a(0(),x) -> c(c(x))
   graph:
    a#(0(),x) -> c#(c(x)) -> c#(c(x)) -> c#(b(c(x)))
    a#(0(),x) -> c#(c(x)) -> c#(c(b(c(x)))) -> a#(0(),c(x))
    a#(0(),x) -> c#(x) -> c#(c(x)) -> c#(b(c(x)))
    a#(0(),x) -> c#(x) -> c#(c(b(c(x)))) -> a#(0(),c(x))
    c#(c(b(c(x)))) -> a#(0(),c(x)) -> a#(0(),x) -> c#(c(x))
    c#(c(b(c(x)))) -> a#(0(),c(x)) -> a#(0(),x) -> c#(x)
    c#(c(x)) -> c#(b(c(x))) -> c#(c(x)) -> c#(b(c(x)))
    c#(c(x)) -> c#(b(c(x))) -> c#(c(b(c(x)))) -> a#(0(),c(x))
   EDG Processor:
    DPs:
     c#(c(b(c(x)))) -> a#(0(),c(x))
     c#(c(x)) -> c#(b(c(x)))
     a#(0(),x) -> c#(x)
     a#(0(),x) -> c#(c(x))
    TRS:
     c(c(b(c(x)))) -> b(a(0(),c(x)))
     c(c(x)) -> b(c(b(c(x))))
     a(0(),x) -> c(c(x))
    graph:
     a#(0(),x) -> c#(c(x)) -> c#(c(b(c(x)))) -> a#(0(),c(x))
     a#(0(),x) -> c#(c(x)) -> c#(c(x)) -> c#(b(c(x)))
     a#(0(),x) -> c#(x) -> c#(c(b(c(x)))) -> a#(0(),c(x))
     a#(0(),x) -> c#(x) -> c#(c(x)) -> c#(b(c(x)))
     c#(c(b(c(x)))) -> a#(0(),c(x)) -> a#(0(),x) -> c#(x)
     c#(c(b(c(x)))) -> a#(0(),c(x)) -> a#(0(),x) -> c#(c(x))
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 6/16
     DPs:
      a#(0(),x) -> c#(c(x))
      c#(c(b(c(x)))) -> a#(0(),c(x))
      a#(0(),x) -> c#(x)
     TRS:
      c(c(b(c(x)))) -> b(a(0(),c(x)))
      c(c(x)) -> b(c(b(c(x))))
      a(0(),x) -> c(c(x))
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       c(c(b(c(x)))) -> b(a(0(),c(x)))
       c(c(x)) -> b(c(b(c(x))))
       a(0(),x) -> c(c(x))
      interpretation:
       [a#](x0, x1) = 2x1,
       
       [c#](x0) = x0,
       
       [a](x0, x1) = 4x1,
       
       [0] = 1,
       
       [b](x0) = x0,
       
       [c](x0) = 2x0
      orientation:
       a#(0(),x) = 2x >= 2x = c#(c(x))
       
       c#(c(b(c(x)))) = 4x >= 4x = a#(0(),c(x))
       
       a#(0(),x) = 2x >= x = c#(x)
       
       c(c(b(c(x)))) = 6x >= 6x = b(a(0(),c(x)))
       
       c(c(x)) = 4x >= 4x = b(c(b(c(x))))
       
       a(0(),x) = 4x >= 4x = c(c(x))
      problem:
       DPs:
        a#(0(),x) -> c#(c(x))
        c#(c(b(c(x)))) -> a#(0(),c(x))
       TRS:
        c(c(b(c(x)))) -> b(a(0(),c(x)))
        c(c(x)) -> b(c(b(c(x))))
        a(0(),x) -> c(c(x))
      Restore Modifier:
       DPs:
        a#(0(),x) -> c#(c(x))
        c#(c(b(c(x)))) -> a#(0(),c(x))
       TRS:
        c(c(b(c(x)))) -> b(a(0(),c(x)))
        c(c(x)) -> b(c(b(c(x))))
        a(0(),x) -> c(c(x))
       Semantic Labeling Processor:
        dimension: 2
        usable rules:
         
        interpretation:
                            [1]
         [a](x0, x1) = x1 + [1],
         
               [0]
         [0] = [1],
         
                   [1 0]     [1]
         [b](x0) = [0 0]x0 + [0],
         
                   [0 1]     [0]
         [c](x0) = [1 0]x0 + [1]
         labeled:
          a#
          c#
         usable (for model):
          a#
          0
          c#
          c
          b
          a
         argument filtering:
          pi(c) = 0
          pi(b) = 0
          pi(0) = []
          pi(a) = 1
          pi(c#) = []
          pi(a#) = []
        precedence:
         a# > c# ~ a ~ 0 ~ b ~ c
        problem:
         DPs:
          
         TRS:
          c(c(b(c(x)))) -> b(a(0(),c(x)))
          c(c(x)) -> b(c(b(c(x))))
          a(0(),x) -> c(c(x))
        Qed