YES
Time: 0.006509
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()}
  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))}
   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:
       
     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()}
    SPSC:
     Simple Projection:
      pi(minus#) = 1
     Strict:
      {}
     Qed