YES
Time: 0.010757
TRS:
 {      pred s x -> x,
   minus(x, s y) -> pred minus(x, y),
   minus(x, 0()) -> x,
  quot(s x, s y) -> s quot(minus(x, y), s y),
  quot(0(), s y) -> 0()}
 DP:
  DP:
   { minus#(x, s y) -> pred# minus(x, y),
     minus#(x, s y) -> minus#(x, y),
    quot#(s x, s y) -> minus#(x, y),
    quot#(s x, s y) -> quot#(minus(x, y), s y)}
  TRS:
  {      pred s x -> x,
    minus(x, s y) -> pred minus(x, y),
    minus(x, 0()) -> x,
   quot(s x, s y) -> s quot(minus(x, y), s y),
   quot(0(), s y) -> 0()}
  UR:
   {     pred s x -> x,
    minus(x, s y) -> pred minus(x, y),
    minus(x, 0()) -> x,
          a(z, w) -> z,
          a(z, w) -> w}
   EDG:
    {(minus#(x, s y) -> minus#(x, y), minus#(x, s y) -> minus#(x, y))
     (minus#(x, s y) -> minus#(x, y), minus#(x, s y) -> pred# minus(x, y))
     (quot#(s x, s y) -> minus#(x, y), minus#(x, s y) -> pred# minus(x, y))
     (quot#(s x, s y) -> minus#(x, y), minus#(x, s y) -> minus#(x, y))
     (quot#(s x, s y) -> quot#(minus(x, y), s y), quot#(s x, s y) -> minus#(x, y))
     (quot#(s x, s y) -> quot#(minus(x, y), s y), quot#(s x, s y) -> quot#(minus(x, y), s y))}
    STATUS:
     arrows: 0.625000
     SCCS (2):
      Scc:
       {quot#(s x, s y) -> quot#(minus(x, y), s y)}
      Scc:
       {minus#(x, s y) -> minus#(x, y)}
      
      SCC (1):
       Strict:
        {quot#(s x, s y) -> quot#(minus(x, y), s y)}
       Weak:
       {      pred s x -> x,
         minus(x, s y) -> pred minus(x, y),
         minus(x, 0()) -> x,
        quot(s x, s y) -> s quot(minus(x, y), s y),
        quot(0(), s y) -> 0()}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [minus](x0, x1) = x0,
         
         [quot](x0, x1) = 0,
         
         [pred](x0) = x0,
         
         [s](x0) = x0 + 1,
         
         [0] = 0,
         
         [quot#](x0, x1) = x0 + 1
        Strict:
         quot#(s x, s y) -> quot#(minus(x, y), s y)
         2 + 1x + 0y >= 1 + 1x + 0y
        Weak:
         quot(0(), s y) -> 0()
         0 + 0y >= 0
         quot(s x, s y) -> s quot(minus(x, y), s y)
         0 + 0x + 0y >= 1 + 0x + 0y
         minus(x, 0()) -> x
         0 + 1x >= 1x
         minus(x, s y) -> pred minus(x, y)
         0 + 1x + 0y >= 0 + 1x + 0y
         pred s x -> x
         1 + 1x >= 1x
       Qed
     
     SCC (1):
      Strict:
       {minus#(x, s y) -> minus#(x, y)}
      Weak:
      {      pred s x -> x,
        minus(x, s y) -> pred minus(x, y),
        minus(x, 0()) -> x,
       quot(s x, s y) -> s quot(minus(x, y), s y),
       quot(0(), s y) -> 0()}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [minus](x0, x1) = 0,
        
        [quot](x0, x1) = x0 + 1,
        
        [pred](x0) = x0 + 1,
        
        [s](x0) = x0 + 1,
        
        [0] = 0,
        
        [minus#](x0, x1) = x0
       Strict:
        minus#(x, s y) -> minus#(x, y)
        1 + 0x + 1y >= 0 + 0x + 1y
       Weak:
        quot(0(), s y) -> 0()
        2 + 1y >= 0
        quot(s x, s y) -> s quot(minus(x, y), s y)
        2 + 0x + 1y >= 3 + 0x + 1y
        minus(x, 0()) -> x
        0 + 0x >= 1x
        minus(x, s y) -> pred minus(x, y)
        0 + 0x + 0y >= 1 + 0x + 0y
        pred s x -> x
        2 + 1x >= 1x
      Qed