YES
Time: 0.020841
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(),
       log s s x -> s log s quot(x, s s 0()),
       log s 0() -> 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),
         log# s s x -> quot#(x, s s 0()),
         log# s s x -> log# s quot(x, s s 0())}
  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(),
        log s s x -> s log s quot(x, s s 0()),
        log s 0() -> 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))
    (log# s s x -> quot#(x, s s 0()), quot#(s x, s y) -> quot#(minus(x, y), s y))
    (log# s s x -> quot#(x, s s 0()), quot#(s 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))
    (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))
    (log# s s x -> log# s quot(x, s s 0()), log# s s x -> quot#(x, s s 0()))
    (log# s s x -> log# s quot(x, s s 0()), log# s s x -> log# s quot(x, s s 0()))}
   SCCS (3):
    Scc:
     {log# s s x -> log# s quot(x, s s 0())}
    Scc:
     {quot#(s x, s y) -> quot#(minus(x, y), s y)}
    Scc:
     {minus#(x, s y) -> minus#(x, y)}
    SCC (1):
     Strict:
      {log# s s x -> log# s quot(x, s s 0())}
     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(),
           log s s x -> s log s quot(x, s s 0()),
           log s 0() -> 0()}
     POLY:
      Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
      Interpretation:
       [minus](x0, x1) = x0,
       
       [quot](x0, x1) = x0,
       
       [pred](x0) = x0,
       
       [s](x0) = x0 + 1,
       
       [log](x0) = x0 + 1,
       
       [0] = 1,
       
       [log#](x0) = x0
      Strict:
       log# s s x -> log# s quot(x, s s 0())
       2 + 1x >= 1 + 1x
      Weak:
       
     Qed
   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(),
          log s s x -> s log s quot(x, s s 0()),
          log s 0() -> 0()}
    POLY:
     Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
     Interpretation:
      [minus](x0, x1) = x0,
      
      [quot](x0, x1) = x0 + 1,
      
      [pred](x0) = x0,
      
      [s](x0) = x0 + 1,
      
      [log](x0) = x0 + 1,
      
      [0] = 1,
      
      [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(),
          log s s x -> s log s quot(x, s s 0()),
          log s 0() -> 0()}
    SPSC:
     Simple Projection:
      pi(minus#) = 1
     Strict:
      {}
     Qed