YES
Time: 0.008322
TRS:
 {*(x, +(y, z)) -> +(*(x, y), *(x, z)),
      *(x, 1()) -> x,
  *(+(x, y), z) -> +(*(x, z), *(y, z)),
      *(1(), y) -> y}
 DP:
  DP:
   {*#(x, +(y, z)) -> *#(x, y),
    *#(x, +(y, z)) -> *#(x, z),
    *#(+(x, y), z) -> *#(x, z),
    *#(+(x, y), z) -> *#(y, z)}
  TRS:
  {*(x, +(y, z)) -> +(*(x, y), *(x, z)),
       *(x, 1()) -> x,
   *(+(x, y), z) -> +(*(x, z), *(y, z)),
       *(1(), y) -> y}
  EDG:
   {(*#(+(x, y), z) -> *#(x, z), *#(+(x, y), z) -> *#(y, z))
    (*#(+(x, y), z) -> *#(x, z), *#(+(x, y), z) -> *#(x, z))
    (*#(+(x, y), z) -> *#(x, z), *#(x, +(y, z)) -> *#(x, z))
    (*#(+(x, y), z) -> *#(x, z), *#(x, +(y, z)) -> *#(x, y))
    (*#(x, +(y, z)) -> *#(x, y), *#(+(x, y), z) -> *#(y, z))
    (*#(x, +(y, z)) -> *#(x, y), *#(+(x, y), z) -> *#(x, z))
    (*#(x, +(y, z)) -> *#(x, y), *#(x, +(y, z)) -> *#(x, z))
    (*#(x, +(y, z)) -> *#(x, y), *#(x, +(y, z)) -> *#(x, y))
    (*#(+(x, y), z) -> *#(y, z), *#(x, +(y, z)) -> *#(x, y))
    (*#(+(x, y), z) -> *#(y, z), *#(x, +(y, z)) -> *#(x, z))
    (*#(+(x, y), z) -> *#(y, z), *#(+(x, y), z) -> *#(x, z))
    (*#(+(x, y), z) -> *#(y, z), *#(+(x, y), z) -> *#(y, z))
    (*#(x, +(y, z)) -> *#(x, z), *#(x, +(y, z)) -> *#(x, y))
    (*#(x, +(y, z)) -> *#(x, z), *#(x, +(y, z)) -> *#(x, z))
    (*#(x, +(y, z)) -> *#(x, z), *#(+(x, y), z) -> *#(x, z))
    (*#(x, +(y, z)) -> *#(x, z), *#(+(x, y), z) -> *#(y, z))}
   STATUS:
    arrows: 0.000000
    SCCS (1):
     Scc:
      {*#(x, +(y, z)) -> *#(x, y),
       *#(x, +(y, z)) -> *#(x, z),
       *#(+(x, y), z) -> *#(x, z),
       *#(+(x, y), z) -> *#(y, z)}
     
     SCC (4):
      Strict:
       {*#(x, +(y, z)) -> *#(x, y),
        *#(x, +(y, z)) -> *#(x, z),
        *#(+(x, y), z) -> *#(x, z),
        *#(+(x, y), z) -> *#(y, z)}
      Weak:
      {*(x, +(y, z)) -> +(*(x, y), *(x, z)),
           *(x, 1()) -> x,
       *(+(x, y), z) -> +(*(x, z), *(y, z)),
           *(1(), y) -> y}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [+](x0, x1) = x0 + x1 + 1,
        
        [*](x0, x1) = x0,
        
        [1] = 0,
        
        [*#](x0, x1) = x0
       Strict:
        *#(+(x, y), z) -> *#(y, z)
        1 + 1x + 1y + 0z >= 0 + 1y + 0z
        *#(+(x, y), z) -> *#(x, z)
        1 + 1x + 1y + 0z >= 0 + 1x + 0z
        *#(x, +(y, z)) -> *#(x, z)
        0 + 1x + 0y + 0z >= 0 + 1x + 0z
        *#(x, +(y, z)) -> *#(x, y)
        0 + 1x + 0y + 0z >= 0 + 1x + 0y
       Weak:
        *(1(), y) -> y
        0 + 0y >= 1y
        *(+(x, y), z) -> +(*(x, z), *(y, z))
        1 + 1x + 1y + 0z >= 1 + 1x + 1y + 0z
        *(x, 1()) -> x
        0 + 1x >= 1x
        *(x, +(y, z)) -> +(*(x, y), *(x, z))
        0 + 1x + 0y + 0z >= 1 + 2x + 0y + 0z
      SCCS (1):
       Scc:
        {*#(x, +(y, z)) -> *#(x, y),
         *#(x, +(y, z)) -> *#(x, z)}
       
       SCC (2):
        Strict:
         {*#(x, +(y, z)) -> *#(x, y),
          *#(x, +(y, z)) -> *#(x, z)}
        Weak:
        {*(x, +(y, z)) -> +(*(x, y), *(x, z)),
             *(x, 1()) -> x,
         *(+(x, y), z) -> +(*(x, z), *(y, z)),
             *(1(), y) -> y}
        POLY:
         Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
         Interpretation:
          [+](x0, x1) = x0 + x1 + 1,
          
          [*](x0, x1) = x0,
          
          [1] = 0,
          
          [*#](x0, x1) = x0
         Strict:
          *#(x, +(y, z)) -> *#(x, z)
          1 + 0x + 1y + 1z >= 0 + 0x + 1z
          *#(x, +(y, z)) -> *#(x, y)
          1 + 0x + 1y + 1z >= 0 + 0x + 1y
         Weak:
          *(1(), y) -> y
          0 + 0y >= 1y
          *(+(x, y), z) -> +(*(x, z), *(y, z))
          1 + 1x + 1y + 0z >= 1 + 1x + 1y + 0z
          *(x, 1()) -> x
          0 + 1x >= 1x
          *(x, +(y, z)) -> +(*(x, y), *(x, z))
          0 + 1x + 0y + 0z >= 1 + 2x + 0y + 0z
        Qed