YES

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

Proof:
 DP Processor:
  DPs:
   a#(x,y) -> c#(y)
   a#(x,y) -> b#(0(),c(y))
   a#(x,y) -> b#(x,b(0(),c(y)))
   c#(b(y,c(x))) -> a#(0(),0())
   c#(b(y,c(x))) -> b#(a(0(),0()),y)
   c#(b(y,c(x))) -> c#(b(a(0(),0()),y))
   c#(b(y,c(x))) -> c#(c(b(a(0(),0()),y)))
  TRS:
   a(x,y) -> b(x,b(0(),c(y)))
   c(b(y,c(x))) -> c(c(b(a(0(),0()),y)))
   b(y,0()) -> y
  Matrix Interpretation Processor: dim=2
   
   usable rules:
    a(x,y) -> b(x,b(0(),c(y)))
    c(b(y,c(x))) -> c(c(b(a(0(),0()),y)))
    b(y,0()) -> y
   interpretation:
    [b#](x0, x1) = [0],
    
    [c#](x0) = [1 0]x0 + [1],
    
    [a#](x0, x1) = [2 2]x0 + [1 2]x1 + [3],
    
                  [2 2]     [0 2]  
    [b](x0, x1) = [0 1]x0 + [0 0]x1,
    
              [0 0]     [3]
    [c](x0) = [1 0]x0 + [2],
    
          [0]
    [0] = [0],
    
                  [2 2]     [2 2]     [1]
    [a](x0, x1) = [0 2]x0 + [2 0]x1 + [0]
   orientation:
    a#(x,y) = [2 2]x + [1 2]y + [3] >= [1 0]y + [1] = c#(y)
    
    a#(x,y) = [2 2]x + [1 2]y + [3] >= [0] = b#(0(),c(y))
    
    a#(x,y) = [2 2]x + [1 2]y + [3] >= [0] = b#(x,b(0(),c(y)))
    
    c#(b(y,c(x))) = [2 0]x + [2 2]y + [5] >= [3] = a#(0(),0())
    
    c#(b(y,c(x))) = [2 0]x + [2 2]y + [5] >= [0] = b#(a(0(),0()),y)
    
    c#(b(y,c(x))) = [2 0]x + [2 2]y + [5] >= [0 2]y + [3] = c#(b(a(0(),0()),y))
    
    c#(b(y,c(x))) = [2 0]x + [2 2]y + [5] >= [4] = c#(c(b(a(0(),0()),y)))
    
             [2 2]    [2 2]    [1]    [2 2]                    
    a(x,y) = [0 2]x + [2 0]y + [0] >= [0 1]x = b(x,b(0(),c(y)))
    
                   [0 0]    [0 0]    [3]    [3]                        
    c(b(y,c(x))) = [2 0]x + [2 2]y + [6] >= [5] = c(c(b(a(0(),0()),y)))
    
               [2 2]          
    b(y,0()) = [0 1]y >= y = y
   problem:
    DPs:
     
    TRS:
     a(x,y) -> b(x,b(0(),c(y)))
     c(b(y,c(x))) -> c(c(b(a(0(),0()),y)))
     b(y,0()) -> y
   Qed