YES
Time: 0.034999
TRS:
 {+(0(), y) -> y,
  +(s x, y) -> +(x, s y),
  +(s x, y) -> s +(x, y)}
 DP:
  DP:
   {+#(s x, y) -> +#(x, y),
    +#(s x, y) -> +#(x, s y)}
  TRS:
  {+(0(), y) -> y,
   +(s x, y) -> +(x, s y),
   +(s x, y) -> s +(x, y)}
  EDG:
   {(+#(s x, y) -> +#(x, y), +#(s x, y) -> +#(x, s y))
    (+#(s x, y) -> +#(x, y), +#(s x, y) -> +#(x, y))
    (+#(s x, y) -> +#(x, s y), +#(s x, y) -> +#(x, y))
    (+#(s x, y) -> +#(x, s y), +#(s x, y) -> +#(x, s y))}
   STATUS:
    arrows: 0.000000
    SCCS (1):
     Scc:
      {+#(s x, y) -> +#(x, y),
       +#(s x, y) -> +#(x, s y)}
     
     SCC (2):
      Strict:
       {+#(s x, y) -> +#(x, y),
        +#(s x, y) -> +#(x, s y)}
      Weak:
      {+(0(), y) -> y,
       +(s x, y) -> +(x, s y),
       +(s x, y) -> s +(x, y)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [+](x0, x1) = x0 + x1 + 1,
        
        [s](x0) = x0 + 1,
        
        [0] = 1,
        
        [+#](x0, x1) = x0 + x1
       Strict:
        +#(s x, y) -> +#(x, s y)
        1 + 1y + 1x >= 1 + 1y + 1x
        +#(s x, y) -> +#(x, y)
        1 + 1y + 1x >= 0 + 1y + 1x
       Weak:
        +(s x, y) -> s +(x, y)
        2 + 1y + 1x >= 2 + 1y + 1x
        +(s x, y) -> +(x, s y)
        2 + 1y + 1x >= 2 + 1y + 1x
        +(0(), y) -> y
        2 + 1y >= 1y
      SCCS (1):
       Scc:
        {+#(s x, y) -> +#(x, s y)}
       
       SCC (1):
        Strict:
         {+#(s x, y) -> +#(x, s y)}
        Weak:
        {+(0(), y) -> y,
         +(s x, y) -> +(x, s y),
         +(s x, y) -> s +(x, y)}
        POLY:
         Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
         Interpretation:
          [+](x0, x1) = 0,
          
          [s](x0) = x0 + 1,
          
          [0] = 0,
          
          [+#](x0, x1) = x0
         Strict:
          +#(s x, y) -> +#(x, s y)
          1 + 0y + 1x >= 0 + 0y + 1x
         Weak:
          +(s x, y) -> s +(x, y)
          0 + 0y + 0x >= 1 + 0y + 0x
          +(s x, y) -> +(x, s y)
          0 + 0y + 0x >= 0 + 0y + 0x
          +(0(), y) -> y
          0 + 0y >= 1y
        Qed