YES
Time: 0.047826
TRS:
 {times(x, 0()) -> 0(),
  times(x, s y) -> plus(times(x, y), x),
   plus(x, 0()) -> x,
   plus(x, s y) -> s plus(x, y),
   plus(0(), x) -> x,
   plus(s x, y) -> s plus(x, y)}
 DP:
  DP:
   {times#(x, s y) -> times#(x, y),
    times#(x, s y) -> plus#(times(x, y), x),
     plus#(x, s y) -> plus#(x, y),
     plus#(s x, y) -> plus#(x, y)}
  TRS:
  {times(x, 0()) -> 0(),
   times(x, s y) -> plus(times(x, y), x),
    plus(x, 0()) -> x,
    plus(x, s y) -> s plus(x, y),
    plus(0(), x) -> x,
    plus(s x, y) -> s plus(x, y)}
  EDG:
   {(times#(x, s y) -> times#(x, y), times#(x, s y) -> plus#(times(x, y), x))
    (times#(x, s y) -> times#(x, y), times#(x, s y) -> times#(x, y))
    (plus#(s x, y) -> plus#(x, y), plus#(s x, y) -> plus#(x, y))
    (plus#(s x, y) -> plus#(x, y), plus#(x, s y) -> plus#(x, y))
    (plus#(x, s y) -> plus#(x, y), plus#(x, s y) -> plus#(x, y))
    (plus#(x, s y) -> plus#(x, y), plus#(s x, y) -> plus#(x, y))
    (times#(x, s y) -> plus#(times(x, y), x), plus#(x, s y) -> plus#(x, y))
    (times#(x, s y) -> plus#(times(x, y), x), plus#(s x, y) -> plus#(x, y))}
   STATUS:
    arrows: 0.500000
    SCCS (2):
     Scc:
      {times#(x, s y) -> times#(x, y)}
     Scc:
      {plus#(x, s y) -> plus#(x, y),
       plus#(s x, y) -> plus#(x, y)}
     
     SCC (1):
      Strict:
       {times#(x, s y) -> times#(x, y)}
      Weak:
      {times(x, 0()) -> 0(),
       times(x, s y) -> plus(times(x, y), x),
        plus(x, 0()) -> x,
        plus(x, s y) -> s plus(x, y),
        plus(0(), x) -> x,
        plus(s x, y) -> s plus(x, y)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [times](x0, x1) = x0 + 1,
        
        [plus](x0, x1) = 0,
        
        [s](x0) = x0 + 1,
        
        [0] = 1,
        
        [times#](x0, x1) = x0
       Strict:
        times#(x, s y) -> times#(x, y)
        1 + 0x + 1y >= 0 + 0x + 1y
       Weak:
        plus(s x, y) -> s plus(x, y)
        0 + 0x + 0y >= 1 + 0x + 0y
        plus(0(), x) -> x
        0 + 0x >= 1x
        plus(x, s y) -> s plus(x, y)
        0 + 0x + 0y >= 1 + 0x + 0y
        plus(x, 0()) -> x
        0 + 0x >= 1x
        times(x, s y) -> plus(times(x, y), x)
        2 + 0x + 1y >= 0 + 0x + 0y
        times(x, 0()) -> 0()
        2 + 0x >= 1
      Qed
    
    SCC (2):
     Strict:
      {plus#(x, s y) -> plus#(x, y),
       plus#(s x, y) -> plus#(x, y)}
     Weak:
     {times(x, 0()) -> 0(),
      times(x, s y) -> plus(times(x, y), x),
       plus(x, 0()) -> x,
       plus(x, s y) -> s plus(x, y),
       plus(0(), x) -> x,
       plus(s x, y) -> s plus(x, y)}
     POLY:
      Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
      Interpretation:
       [times](x0, x1) = x0 + 1,
       
       [plus](x0, x1) = 0,
       
       [s](x0) = x0 + 1,
       
       [0] = 1,
       
       [plus#](x0, x1) = x0
      Strict:
       plus#(s x, y) -> plus#(x, y)
       0 + 0x + 1y >= 0 + 0x + 1y
       plus#(x, s y) -> plus#(x, y)
       1 + 0x + 1y >= 0 + 0x + 1y
      Weak:
       plus(s x, y) -> s plus(x, y)
       0 + 0x + 0y >= 1 + 0x + 0y
       plus(0(), x) -> x
       0 + 0x >= 1x
       plus(x, s y) -> s plus(x, y)
       0 + 0x + 0y >= 1 + 0x + 0y
       plus(x, 0()) -> x
       0 + 0x >= 1x
       times(x, s y) -> plus(times(x, y), x)
       2 + 0x + 1y >= 0 + 0x + 0y
       times(x, 0()) -> 0()
       2 + 0x >= 1
     SCCS (1):
      Scc:
       {plus#(s x, y) -> plus#(x, y)}
      
      SCC (1):
       Strict:
        {plus#(s x, y) -> plus#(x, y)}
       Weak:
       {times(x, 0()) -> 0(),
        times(x, s y) -> plus(times(x, y), x),
         plus(x, 0()) -> x,
         plus(x, s y) -> s plus(x, y),
         plus(0(), x) -> x,
         plus(s x, y) -> s plus(x, y)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [times](x0, x1) = x0 + 1,
         
         [plus](x0, x1) = 0,
         
         [s](x0) = x0 + 1,
         
         [0] = 1,
         
         [plus#](x0, x1) = x0
        Strict:
         plus#(s x, y) -> plus#(x, y)
         1 + 1x + 0y >= 0 + 1x + 0y
        Weak:
         plus(s x, y) -> s plus(x, y)
         0 + 0x + 0y >= 1 + 0x + 0y
         plus(0(), x) -> x
         0 + 0x >= 1x
         plus(x, s y) -> s plus(x, y)
         0 + 0x + 0y >= 1 + 0x + 0y
         plus(x, 0()) -> x
         0 + 0x >= 1x
         times(x, s y) -> plus(times(x, y), x)
         2 + 0x + 1y >= 0 + 0x + 0y
         times(x, 0()) -> 0()
         2 + 0x >= 1
       Qed