YES
Time: 0.039561
TRS:
 {ack(s x, s y) -> ack(x, ack(s x, y)),
  ack(s x, 0()) -> ack(x, s 0()),
    ack(0(), y) -> s y}
 DP:
  DP:
   {ack#(s x, s y) -> ack#(x, ack(s x, y)),
    ack#(s x, s y) -> ack#(s x, y),
    ack#(s x, 0()) -> ack#(x, s 0())}
  TRS:
  {ack(s x, s y) -> ack(x, ack(s x, y)),
   ack(s x, 0()) -> ack(x, s 0()),
     ack(0(), y) -> s y}
  UR:
   {ack(s x, s y) -> ack(x, ack(s x, y)),
    ack(s x, 0()) -> ack(x, s 0()),
      ack(0(), y) -> s y,
          a(z, w) -> z,
          a(z, w) -> w}
   EDG:
    {(ack#(s x, s y) -> ack#(s x, y), ack#(s x, 0()) -> ack#(x, s 0()))
     (ack#(s x, s y) -> ack#(s x, y), ack#(s x, s y) -> ack#(s x, y))
     (ack#(s x, s y) -> ack#(s x, y), ack#(s x, s y) -> ack#(x, ack(s x, y)))
     (ack#(s x, 0()) -> ack#(x, s 0()), ack#(s x, s y) -> ack#(x, ack(s x, y)))
     (ack#(s x, 0()) -> ack#(x, s 0()), ack#(s x, s y) -> ack#(s x, y))
     (ack#(s x, s y) -> ack#(x, ack(s x, y)), ack#(s x, s y) -> ack#(x, ack(s x, y)))
     (ack#(s x, s y) -> ack#(x, ack(s x, y)), ack#(s x, s y) -> ack#(s x, y))
     (ack#(s x, s y) -> ack#(x, ack(s x, y)), ack#(s x, 0()) -> ack#(x, s 0()))}
    STATUS:
     arrows: 0.111111
     SCCS (1):
      Scc:
       {ack#(s x, s y) -> ack#(x, ack(s x, y)),
        ack#(s x, s y) -> ack#(s x, y),
        ack#(s x, 0()) -> ack#(x, s 0())}
      
      SCC (3):
       Strict:
        {ack#(s x, s y) -> ack#(x, ack(s x, y)),
         ack#(s x, s y) -> ack#(s x, y),
         ack#(s x, 0()) -> ack#(x, s 0())}
       Weak:
       {ack(s x, s y) -> ack(x, ack(s x, y)),
        ack(s x, 0()) -> ack(x, s 0()),
          ack(0(), y) -> s y}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [ack](x0, x1) = x0,
         
         [s](x0) = x0 + 1,
         
         [0] = 1,
         
         [ack#](x0, x1) = x0
        Strict:
         ack#(s x, 0()) -> ack#(x, s 0())
         1 + 1x >= 0 + 1x
         ack#(s x, s y) -> ack#(s x, y)
         1 + 0y + 1x >= 1 + 0y + 1x
         ack#(s x, s y) -> ack#(x, ack(s x, y))
         1 + 0y + 1x >= 0 + 0y + 1x
        Weak:
         ack(0(), y) -> s y
         0 + 1y >= 1 + 1y
         ack(s x, 0()) -> ack(x, s 0())
         1 + 0x >= 2 + 0x
         ack(s x, s y) -> ack(x, ack(s x, y))
         1 + 1y + 0x >= 0 + 1y + 0x
       SCCS (1):
        Scc:
         {ack#(s x, s y) -> ack#(s x, y)}
        
        SCC (1):
         Strict:
          {ack#(s x, s y) -> ack#(s x, y)}
         Weak:
         {ack(s x, s y) -> ack(x, ack(s x, y)),
          ack(s x, 0()) -> ack(x, s 0()),
            ack(0(), y) -> s y}
         POLY:
          Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
          Interpretation:
           [ack](x0, x1) = x0 + x1 + 1,
           
           [s](x0) = x0 + 1,
           
           [0] = 1,
           
           [ack#](x0, x1) = x0 + 1
          Strict:
           ack#(s x, s y) -> ack#(s x, y)
           2 + 1y + 0x >= 1 + 1y + 0x
          Weak:
           ack(0(), y) -> s y
           2 + 1y >= 1 + 1y
           ack(s x, 0()) -> ack(x, s 0())
           3 + 1x >= 3 + 1x
           ack(s x, s y) -> ack(x, ack(s x, y))
           3 + 1y + 1x >= 3 + 1y + 2x
         Qed