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))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
       [a#](x0, x1) = [0 0 1]x0 + [2 2 0]x1 + [2],
       
       [c#](x0) = [0 2 0]x0,
       
                     [0 0 0]     [2 2 0]     [2]
       [a](x0, x1) = [0 0 2]x0 + [1 3 0]x1 + [2]
                     [0 1 0]     [1 3 0]     [0],
       
             [0]
       [0] = [1]
             [1],
       
                 [1 0 0]     [2]
       [b](x0) = [0 0 1]x0 + [0]
                 [0 0 0]     [1],
       
                 [0 2 0]     [0]
       [c](x0) = [1 1 0]x0 + [1]
                 [1 1 0]     [0]
      orientation:
       a#(0(),x) = [2 2 0]x + [3] >= [2 2 0]x + [2] = c#(c(x))
       
       c#(c(b(c(x)))) = [2 6 0]x + [6] >= [2 6 0]x + [5] = a#(0(),c(x))
       
       a#(0(),x) = [2 2 0]x + [3] >= [0 2 0]x = c#(x)
       
                       [2 6 0]    [6]    [2 6 0]    [6]                 
       c(c(b(c(x)))) = [3 5 0]x + [4] >= [3 5 0]x + [4] = b(a(0(),c(x)))
                       [3 5 0]    [3]    [0 0 0]    [1]                 
       
                 [2 2 0]    [2]    [2 2 0]    [2]                
       c(c(x)) = [1 3 0]x + [2] >= [1 3 0]x + [2] = b(c(b(c(x))))
                 [1 3 0]    [1]    [0 0 0]    [1]                
       
                  [2 2 0]    [2]    [2 2 0]    [2]          
       a(0(),x) = [1 3 0]x + [4] >= [1 3 0]x + [2] = c(c(x))
                  [1 3 0]    [1]    [1 3 0]    [1]          
      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