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
     Matrix Interpretation Processor: dim=3
      
      interpretation:
       [c#](x0) = [1 0 2]x0,
       
                     [2 0 0]     [0 1 1]     [1]
       [a](x0, x1) = [0 0 0]x0 + [0 2 0]x1 + [0]
                     [0 0 0]     [0 0 0]     [0],
       
             [0]
       [0] = [0]
             [0],
       
                 [1 0 1]     [0]
       [c](x0) = [1 1 1]x0 + [1]
                 [0 1 1]     [0]
      orientation:
       c#(a(a(0(),x),y)) = [0 2 2]x + [0 1 1]y + [3] >= [2] = c#(c(c(0())))
       
       c#(c(c(y))) = [3 5 6]y + [2] >= [2 0 0]y + [1] = c#(a(y,0()))
       
       c#(c(c(y))) = [3 5 6]y + [2] >= [2 0 0]y + [1] = c#(c(a(y,0())))
       
                    [2 3 4]    [1]    [2 0 0]    [1]                 
       c(c(c(y))) = [4 5 7]y + [4] >= [4 0 0]y + [4] = c(c(a(y,0())))
                    [3 4 5]    [3]    [2 0 0]    [2]                 
       
                          [0 2 2]    [0 1 1]    [3]    [0 1 1]    [3]                    
       c(a(a(0(),x),y)) = [0 2 2]x + [0 3 1]y + [4] >= [0 2 0]y + [0] = a(c(c(c(0()))),y)
                          [0 0 0]    [0 2 0]    [0]    [0 0 0]    [0]                    
       
              [1 0 1]    [0]         
       c(y) = [1 1 1]y + [1] >= y = y
              [0 1 1]    [0]         
      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