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
      interpretation:
       [a#](x0, x1) = 4x1 + -2,
       
       [c#](x0) = 2x0,
       
       [a](x0, x1) = -4x0 + 4x1 + 0,
       
       [0] = 4,
       
       [b](x0) = x0 + -16,
       
       [c](x0) = 2x0 + -4
      orientation:
       a#(0(),x) = 4x + -2 >= 4x + -2 = c#(c(x))
       
       c#(c(b(c(x)))) = 6x + 0 >= 6x + 0 = a#(0(),c(x))
       
       a#(0(),x) = 4x + -2 >= 2x = c#(x)
       
       c(c(b(c(x)))) = 6x + 0 >= 6x + 0 = b(a(0(),c(x)))
       
       c(c(x)) = 4x + -2 >= 4x + -2 = b(c(b(c(x))))
       
       a(0(),x) = 4x + 0 >= 4x + -2 = 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))
      Matrix Interpretation Processor: dim=2
       
       interpretation:
        [a#](x0, x1) = [1 2]x0 + [2 0]x1 + [2],
        
        [c#](x0) = [0 2]x0,
        
                      [0 2]     [1 0]     [0]
        [a](x0, x1) = [3 0]x0 + [3 1]x1 + [1],
        
              [1]
        [0] = [1],
        
                  [1 0]     [1]
        [b](x0) = [0 0]x0 + [0],
        
                  [0 1]     [0]
        [c](x0) = [1 0]x0 + [2]
       orientation:
        a#(0(),x) = [2 0]x + [5] >= [2 0]x + [4] = c#(c(x))
        
        c#(c(b(c(x)))) = [0 2]x + [6] >= [0 2]x + [5] = a#(0(),c(x))
        
                        [0 1]    [3]    [0 1]    [3]                 
        c(c(b(c(x)))) = [0 0]x + [2] >= [0 0]x + [0] = b(a(0(),c(x)))
        
                      [2]    [1]                
        c(c(x)) = x + [2] >= [0] = b(c(b(c(x))))
        
                   [1 0]    [2]        [2]          
        a(0(),x) = [3 1]x + [4] >= x + [2] = c(c(x))
       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