YES

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

Proof:
 DP Processor:
  DPs:
   c#(c(c(y))) -> c#(a(y,0()))
   c#(c(c(y))) -> c#(c(a(y,0())))
   c#(a(a(0(),x),y)) -> c#(0())
   c#(a(a(0(),x),y)) -> c#(c(0()))
   c#(a(a(0(),x),y)) -> c#(c(c(0())))
  TRS:
   c(c(c(y))) -> c(c(a(y,0())))
   c(a(a(0(),x),y)) -> a(c(c(c(0()))),y)
   c(y) -> y
  EDG Processor:
   DPs:
    c#(c(c(y))) -> c#(a(y,0()))
    c#(c(c(y))) -> c#(c(a(y,0())))
    c#(a(a(0(),x),y)) -> c#(0())
    c#(a(a(0(),x),y)) -> c#(c(0()))
    c#(a(a(0(),x),y)) -> c#(c(c(0())))
   TRS:
    c(c(c(y))) -> c(c(a(y,0())))
    c(a(a(0(),x),y)) -> a(c(c(c(0()))),y)
    c(y) -> y
   graph:
    c#(a(a(0(),x),y)) -> c#(c(0())) -> c#(c(c(y))) -> c#(a(y,0()))
    c#(a(a(0(),x),y)) -> c#(c(0())) ->
    c#(c(c(y))) -> c#(c(a(y,0())))
    c#(a(a(0(),x),y)) -> c#(c(0())) -> c#(a(a(0(),x),y)) -> c#(0())
    c#(a(a(0(),x),y)) -> c#(c(0())) ->
    c#(a(a(0(),x),y)) -> c#(c(0()))
    c#(a(a(0(),x),y)) -> c#(c(0())) ->
    c#(a(a(0(),x),y)) -> c#(c(c(0())))
    c#(a(a(0(),x),y)) -> c#(c(c(0()))) ->
    c#(c(c(y))) -> c#(a(y,0()))
    c#(a(a(0(),x),y)) -> c#(c(c(0()))) ->
    c#(c(c(y))) -> c#(c(a(y,0())))
    c#(a(a(0(),x),y)) -> c#(c(c(0()))) ->
    c#(a(a(0(),x),y)) -> c#(0())
    c#(a(a(0(),x),y)) -> c#(c(c(0()))) ->
    c#(a(a(0(),x),y)) -> c#(c(0()))
    c#(a(a(0(),x),y)) -> c#(c(c(0()))) ->
    c#(a(a(0(),x),y)) -> c#(c(c(0())))
    c#(c(c(y))) -> c#(a(y,0())) -> c#(a(a(0(),x),y)) -> c#(0())
    c#(c(c(y))) -> c#(a(y,0())) -> c#(a(a(0(),x),y)) -> c#(c(0()))
    c#(c(c(y))) -> c#(a(y,0())) -> c#(a(a(0(),x),y)) -> c#(c(c(0())))
    c#(c(c(y))) -> c#(c(a(y,0()))) -> c#(c(c(y))) -> c#(a(y,0()))
    c#(c(c(y))) -> c#(c(a(y,0()))) -> c#(c(c(y))) -> c#(c(a(y,0())))
    c#(c(c(y))) -> c#(c(a(y,0()))) -> c#(a(a(0(),x),y)) -> c#(0())
    c#(c(c(y))) -> c#(c(a(y,0()))) -> c#(a(a(0(),x),y)) -> c#(c(0()))
    c#(c(c(y))) -> c#(c(a(y,0()))) -> c#(a(a(0(),x),y)) -> c#(c(c(0())))
   CDG Processor:
    DPs:
     c#(c(c(y))) -> c#(a(y,0()))
     c#(c(c(y))) -> c#(c(a(y,0())))
     c#(a(a(0(),x),y)) -> c#(0())
     c#(a(a(0(),x),y)) -> c#(c(0()))
     c#(a(a(0(),x),y)) -> c#(c(c(0())))
    TRS:
     c(c(c(y))) -> c(c(a(y,0())))
     c(a(a(0(),x),y)) -> a(c(c(c(0()))),y)
     c(y) -> y
    graph:
     c#(a(a(0(),x),y)) -> c#(c(c(0()))) ->
     c#(a(a(0(),x),y)) -> c#(c(c(0())))
     c#(a(a(0(),x),y)) -> c#(c(c(0()))) ->
     c#(a(a(0(),x),y)) -> c#(c(0()))
     c#(a(a(0(),x),y)) -> c#(c(c(0()))) ->
     c#(a(a(0(),x),y)) -> c#(0())
     c#(a(a(0(),x),y)) -> c#(c(c(0()))) ->
     c#(c(c(y))) -> c#(c(a(y,0())))
     c#(a(a(0(),x),y)) -> c#(c(c(0()))) -> c#(c(c(y))) -> c#(a(y,0()))
     c#(c(c(y))) -> c#(a(y,0())) -> c#(a(a(0(),x),y)) -> c#(c(c(0())))
     c#(c(c(y))) -> c#(a(y,0())) -> c#(a(a(0(),x),y)) -> c#(c(0()))
     c#(c(c(y))) -> c#(a(y,0())) -> c#(a(a(0(),x),y)) -> c#(0())
     c#(c(c(y))) -> c#(c(a(y,0()))) ->
     c#(a(a(0(),x),y)) -> c#(c(c(0())))
     c#(c(c(y))) -> c#(c(a(y,0()))) ->
     c#(a(a(0(),x),y)) -> c#(c(0()))
     c#(c(c(y))) -> c#(c(a(y,0()))) -> c#(a(a(0(),x),y)) -> c#(0())
     c#(c(c(y))) -> c#(c(a(y,0()))) -> c#(c(c(y))) -> c#(c(a(y,0())))
     c#(c(c(y))) -> c#(c(a(y,0()))) -> c#(c(c(y))) -> c#(a(y,0()))
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 13/25
     DPs:
      c#(a(a(0(),x),y)) -> c#(c(c(0())))
      c#(c(c(y))) -> c#(a(y,0()))
      c#(c(c(y))) -> c#(c(a(y,0())))
     TRS:
      c(c(c(y))) -> c(c(a(y,0())))
      c(a(a(0(),x),y)) -> a(c(c(c(0()))),y)
      c(y) -> y
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [c#](x0) = [0 0]x0 + [0],
       
                     [0  -&]     [0  -&]     [0]
       [a](x0, x1) = [0  1 ]x0 + [2  0 ]x1 + [0],
       
             [0]
       [0] = [1],
       
                 [1 0]     [1]
       [c](x0) = [0 0]x0 + [0]
      orientation:
       c#(a(a(0(),x),y)) = [3 1]x + [2 0]y + [3] >= [2] = c#(c(c(0())))
       
       c#(c(c(y))) = [2 1]y + [2] >= [0 1]y + [2] = c#(a(y,0()))
       
       c#(c(c(y))) = [2 1]y + [2] >= [1 1]y + [2] = c#(c(a(y,0())))
       
                    [3 2]    [3]    [2 2]    [3]                 
       c(c(c(y))) = [2 1]y + [2] >= [1 1]y + [2] = c(c(a(y,0())))
       
                          [3 1]    [2 0]    [3]    [0  -&]    [3]                    
       c(a(a(0(),x),y)) = [3 1]x + [2 0]y + [3] >= [2  0 ]y + [3] = a(c(c(c(0()))),y)
       
              [1 0]    [1]         
       c(y) = [0 0]y + [0] >= y = y
      problem:
       DPs:
        c#(c(c(y))) -> c#(a(y,0()))
        c#(c(c(y))) -> c#(c(a(y,0())))
       TRS:
        c(c(c(y))) -> c(c(a(y,0())))
        c(a(a(0(),x),y)) -> a(c(c(c(0()))),y)
        c(y) -> y
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 7/4
       DPs:
        c#(c(c(y))) -> c#(c(a(y,0())))
       TRS:
        c(c(c(y))) -> c(c(a(y,0())))
        c(a(a(0(),x),y)) -> a(c(c(c(0()))),y)
        c(y) -> y
       Arctic Interpretation Processor:
        dimension: 1
        interpretation:
         [c#](x0) = 2x0 + 5,
         
         [a](x0, x1) = x1,
         
         [0] = 0,
         
         [c](x0) = 2x0 + 2
        orientation:
         c#(c(c(y))) = 6y + 6 >= 5 = c#(c(a(y,0())))
         
         c(c(c(y))) = 6y + 6 >= 4 = c(c(a(y,0())))
         
         c(a(a(0(),x),y)) = 2y + 2 >= y = a(c(c(c(0()))),y)
         
         c(y) = 2y + 2 >= y = y
        problem:
         DPs:
          
         TRS:
          c(c(c(y))) -> c(c(a(y,0())))
          c(a(a(0(),x),y)) -> a(c(c(c(0()))),y)
          c(y) -> y
        Qed