YES
Time: 0.001041
TRS:
 {  bin(x, 0()) -> s 0(),
  bin(s x, s y) -> +(bin(x, s y), bin(x, y)),
  bin(0(), s y) -> 0()}
 DP:
  DP:
   {bin#(s x, s y) -> bin#(x, y),
    bin#(s x, s y) -> bin#(x, s y)}
  TRS:
  {  bin(x, 0()) -> s 0(),
   bin(s x, s y) -> +(bin(x, s y), bin(x, y)),
   bin(0(), s y) -> 0()}
  EDG:
   {(bin#(s x, s y) -> bin#(x, y), bin#(s x, s y) -> bin#(x, s y))
    (bin#(s x, s y) -> bin#(x, y), bin#(s x, s y) -> bin#(x, y))
    (bin#(s x, s y) -> bin#(x, s y), bin#(s x, s y) -> bin#(x, y))
    (bin#(s x, s y) -> bin#(x, s y), bin#(s x, s y) -> bin#(x, s y))}
   SCCS (1):
    Scc:
     {bin#(s x, s y) -> bin#(x, y),
      bin#(s x, s y) -> bin#(x, s y)}
    SCC (2):
     Strict:
      {bin#(s x, s y) -> bin#(x, y),
       bin#(s x, s y) -> bin#(x, s y)}
     Weak:
     {  bin(x, 0()) -> s 0(),
      bin(s x, s y) -> +(bin(x, s y), bin(x, y)),
      bin(0(), s y) -> 0()}
     SPSC:
      Simple Projection:
       pi(bin#) = 1
      Strict:
       {bin#(s x, s y) -> bin#(x, s y)}
      EDG:
       {(bin#(s x, s y) -> bin#(x, s y), bin#(s x, s y) -> bin#(x, s y))}
       SCCS (1):
        Scc:
         {bin#(s x, s y) -> bin#(x, s y)}
        SCC (1):
         Strict:
          {bin#(s x, s y) -> bin#(x, s y)}
         Weak:
         {  bin(x, 0()) -> s 0(),
          bin(s x, s y) -> +(bin(x, s y), bin(x, y)),
          bin(0(), s y) -> 0()}
         SPSC:
          Simple Projection:
           pi(bin#) = 0
          Strict:
           {}
          Qed