YES

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

Proof:
 DP Processor:
  DPs:
   c#(c(c(a(x,y)))) -> c#(y)
   c#(c(c(a(x,y)))) -> c#(c(y))
   c#(c(c(a(x,y)))) -> c#(c(c(y)))
   c#(c(c(a(x,y)))) -> c#(c(c(c(y))))
   c#(c(b(c(y),0()))) -> c#(a(y,0()))
   c#(c(b(c(y),0()))) -> c#(c(a(y,0())))
   c#(c(a(a(y,0()),x))) -> c#(y)
  TRS:
   c(c(c(a(x,y)))) -> b(c(c(c(c(y)))),x)
   c(c(b(c(y),0()))) -> a(0(),c(c(a(y,0()))))
   c(c(a(a(y,0()),x))) -> c(y)
  EDG Processor:
   DPs:
    c#(c(c(a(x,y)))) -> c#(y)
    c#(c(c(a(x,y)))) -> c#(c(y))
    c#(c(c(a(x,y)))) -> c#(c(c(y)))
    c#(c(c(a(x,y)))) -> c#(c(c(c(y))))
    c#(c(b(c(y),0()))) -> c#(a(y,0()))
    c#(c(b(c(y),0()))) -> c#(c(a(y,0())))
    c#(c(a(a(y,0()),x))) -> c#(y)
   TRS:
    c(c(c(a(x,y)))) -> b(c(c(c(c(y)))),x)
    c(c(b(c(y),0()))) -> a(0(),c(c(a(y,0()))))
    c(c(a(a(y,0()),x))) -> c(y)
   graph:
    c#(c(b(c(y),0()))) -> c#(c(a(y,0()))) ->
    c#(c(a(a(y,0()),x))) -> c#(y)
    c#(c(c(a(x,y)))) -> c#(c(c(c(y)))) ->
    c#(c(c(a(x,y)))) -> c#(y)
    c#(c(c(a(x,y)))) -> c#(c(c(c(y)))) ->
    c#(c(c(a(x,y)))) -> c#(c(y))
    c#(c(c(a(x,y)))) -> c#(c(c(c(y)))) ->
    c#(c(c(a(x,y)))) -> c#(c(c(y)))
    c#(c(c(a(x,y)))) -> c#(c(c(c(y)))) ->
    c#(c(c(a(x,y)))) -> c#(c(c(c(y))))
    c#(c(c(a(x,y)))) -> c#(c(c(c(y)))) ->
    c#(c(b(c(y),0()))) -> c#(a(y,0()))
    c#(c(c(a(x,y)))) -> c#(c(c(c(y)))) ->
    c#(c(b(c(y),0()))) -> c#(c(a(y,0())))
    c#(c(c(a(x,y)))) -> c#(c(c(c(y)))) ->
    c#(c(a(a(y,0()),x))) -> c#(y)
    c#(c(c(a(x,y)))) -> c#(c(c(y))) -> c#(c(c(a(x,y)))) -> c#(y)
    c#(c(c(a(x,y)))) -> c#(c(c(y))) -> c#(c(c(a(x,y)))) -> c#(c(y))
    c#(c(c(a(x,y)))) -> c#(c(c(y))) ->
    c#(c(c(a(x,y)))) -> c#(c(c(y)))
    c#(c(c(a(x,y)))) -> c#(c(c(y))) ->
    c#(c(c(a(x,y)))) -> c#(c(c(c(y))))
    c#(c(c(a(x,y)))) -> c#(c(c(y))) ->
    c#(c(b(c(y),0()))) -> c#(a(y,0()))
    c#(c(c(a(x,y)))) -> c#(c(c(y))) ->
    c#(c(b(c(y),0()))) -> c#(c(a(y,0())))
    c#(c(c(a(x,y)))) -> c#(c(c(y))) -> c#(c(a(a(y,0()),x))) -> c#(y)
    c#(c(c(a(x,y)))) -> c#(c(y)) -> c#(c(c(a(x,y)))) -> c#(y)
    c#(c(c(a(x,y)))) -> c#(c(y)) -> c#(c(c(a(x,y)))) -> c#(c(y))
    c#(c(c(a(x,y)))) -> c#(c(y)) -> c#(c(c(a(x,y)))) -> c#(c(c(y)))
    c#(c(c(a(x,y)))) -> c#(c(y)) -> c#(c(c(a(x,y)))) -> c#(c(c(c(y))))
    c#(c(c(a(x,y)))) -> c#(c(y)) -> c#(c(b(c(y),0()))) -> c#(a(y,0()))
    c#(c(c(a(x,y)))) -> c#(c(y)) ->
    c#(c(b(c(y),0()))) -> c#(c(a(y,0())))
    c#(c(c(a(x,y)))) -> c#(c(y)) -> c#(c(a(a(y,0()),x))) -> c#(y)
    c#(c(c(a(x,y)))) -> c#(y) -> c#(c(c(a(x,y)))) -> c#(y)
    c#(c(c(a(x,y)))) -> c#(y) -> c#(c(c(a(x,y)))) -> c#(c(y))
    c#(c(c(a(x,y)))) -> c#(y) -> c#(c(c(a(x,y)))) -> c#(c(c(y)))
    c#(c(c(a(x,y)))) -> c#(y) -> c#(c(c(a(x,y)))) -> c#(c(c(c(y))))
    c#(c(c(a(x,y)))) -> c#(y) -> c#(c(b(c(y),0()))) -> c#(a(y,0()))
    c#(c(c(a(x,y)))) -> c#(y) -> c#(c(b(c(y),0()))) -> c#(c(a(y,0())))
    c#(c(c(a(x,y)))) -> c#(y) -> c#(c(a(a(y,0()),x))) -> c#(y)
    c#(c(a(a(y,0()),x))) -> c#(y) -> c#(c(c(a(x,y)))) -> c#(y)
    c#(c(a(a(y,0()),x))) -> c#(y) -> c#(c(c(a(x,y)))) -> c#(c(y))
    c#(c(a(a(y,0()),x))) -> c#(y) -> c#(c(c(a(x,y)))) -> c#(c(c(y)))
    c#(c(a(a(y,0()),x))) -> c#(y) ->
    c#(c(c(a(x,y)))) -> c#(c(c(c(y))))
    c#(c(a(a(y,0()),x))) -> c#(y) ->
    c#(c(b(c(y),0()))) -> c#(a(y,0()))
    c#(c(a(a(y,0()),x))) -> c#(y) ->
    c#(c(b(c(y),0()))) -> c#(c(a(y,0())))
    c#(c(a(a(y,0()),x))) -> c#(y) -> c#(c(a(a(y,0()),x))) -> c#(y)
   SCC Processor:
    #sccs: 1
    #rules: 6
    #arcs: 36/49
    DPs:
     c#(c(b(c(y),0()))) -> c#(c(a(y,0())))
     c#(c(a(a(y,0()),x))) -> c#(y)
     c#(c(c(a(x,y)))) -> c#(c(c(c(y))))
     c#(c(c(a(x,y)))) -> c#(c(c(y)))
     c#(c(c(a(x,y)))) -> c#(c(y))
     c#(c(c(a(x,y)))) -> c#(y)
    TRS:
     c(c(c(a(x,y)))) -> b(c(c(c(c(y)))),x)
     c(c(b(c(y),0()))) -> a(0(),c(c(a(y,0()))))
     c(c(a(a(y,0()),x))) -> c(y)
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [c#](x0) = x0 + 1,
      
      [0] = 2,
      
      [b](x0, x1) = x0 + 3x1 + 0,
      
      [c](x0) = 1x0 + 0,
      
      [a](x0, x1) = x0 + 1x1 + 0
     orientation:
      c#(c(b(c(y),0()))) = 2y + 6 >= 1y + 4 = c#(c(a(y,0())))
      
      c#(c(a(a(y,0()),x))) = 2x + 1y + 4 >= y + 1 = c#(y)
      
      c#(c(c(a(x,y)))) = 2x + 3y + 2 >= 3y + 2 = c#(c(c(c(y))))
      
      c#(c(c(a(x,y)))) = 2x + 3y + 2 >= 2y + 1 = c#(c(c(y)))
      
      c#(c(c(a(x,y)))) = 2x + 3y + 2 >= 1y + 1 = c#(c(y))
      
      c#(c(c(a(x,y)))) = 2x + 3y + 2 >= y + 1 = c#(y)
      
      c(c(c(a(x,y)))) = 3x + 4y + 3 >= 3x + 4y + 3 = b(c(c(c(c(y)))),x)
      
      c(c(b(c(y),0()))) = 3y + 7 >= 3y + 6 = a(0(),c(c(a(y,0()))))
      
      c(c(a(a(y,0()),x))) = 3x + 2y + 5 >= 1y + 0 = c(y)
     problem:
      DPs:
       c#(c(c(a(x,y)))) -> c#(c(c(c(y))))
      TRS:
       c(c(c(a(x,y)))) -> b(c(c(c(c(y)))),x)
       c(c(b(c(y),0()))) -> a(0(),c(c(a(y,0()))))
       c(c(a(a(y,0()),x))) -> c(y)
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [c#](x0) = x0 + 0,
       
       [0] = 0,
       
       [b](x0, x1) = 1x0 + 2x1 + 4,
       
       [c](x0) = 1x0 + 0,
       
       [a](x0, x1) = x0 + 2x1 + 2
      orientation:
       c#(c(c(a(x,y)))) = 2x + 4y + 4 >= 3y + 2 = c#(c(c(c(y))))
       
       c(c(c(a(x,y)))) = 3x + 5y + 5 >= 2x + 5y + 4 = b(c(c(c(c(y)))),x)
       
       c(c(b(c(y),0()))) = 4y + 6 >= 4y + 6 = a(0(),c(c(a(y,0()))))
       
       c(c(a(a(y,0()),x))) = 4x + 2y + 4 >= 1y + 0 = c(y)
      problem:
       DPs:
        
       TRS:
        c(c(c(a(x,y)))) -> b(c(c(c(c(y)))),x)
        c(c(b(c(y),0()))) -> a(0(),c(c(a(y,0()))))
        c(c(a(a(y,0()),x))) -> c(y)
      Qed