YES
Time: 0.020784
TRS:
 {   min(X, 0()) -> X,
   min(s X, s Y) -> min(X, Y),
  quot(0(), s Y) -> 0(),
  quot(s X, s Y) -> s quot(min(X, Y), s Y),
       log s 0() -> 0(),
       log s s X -> s log s quot(X, s s 0())}
 DP:
  DP:
   { min#(s X, s Y) -> min#(X, Y),
    quot#(s X, s Y) -> min#(X, Y),
    quot#(s X, s Y) -> quot#(min(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:
  {   min(X, 0()) -> X,
    min(s X, s Y) -> min(X, Y),
   quot(0(), s Y) -> 0(),
   quot(s X, s Y) -> s quot(min(X, Y), s Y),
        log s 0() -> 0(),
        log s s X -> s log s quot(X, s s 0())}
  EDG:
   {(quot#(s X, s Y) -> min#(X, Y), min#(s X, s Y) -> min#(X, Y))
    (quot#(s X, s Y) -> quot#(min(X, Y), s Y), quot#(s X, s Y) -> quot#(min(X, Y), s Y))
    (quot#(s X, s Y) -> quot#(min(X, Y), s Y), quot#(s X, s Y) -> min#(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()))
    (log# s s X -> quot#(X, s s 0()), quot#(s X, s Y) -> min#(X, Y))
    (log# s s X -> quot#(X, s s 0()), quot#(s X, s Y) -> quot#(min(X, Y), s Y))
    (min#(s X, s Y) -> min#(X, Y), min#(s X, s Y) -> min#(X, Y))}
   SCCS (3):
    Scc:
     {log# s s X -> log# s quot(X, s s 0())}
    Scc:
     {quot#(s X, s Y) -> quot#(min(X, Y), s Y)}
    Scc:
     {min#(s X, s Y) -> min#(X, Y)}
    SCC (1):
     Strict:
      {log# s s X -> log# s quot(X, s s 0())}
     Weak:
     {   min(X, 0()) -> X,
       min(s X, s Y) -> min(X, Y),
      quot(0(), s Y) -> 0(),
      quot(s X, s Y) -> s quot(min(X, Y), s Y),
           log s 0() -> 0(),
           log s s X -> s log s quot(X, s s 0())}
     POLY:
      Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
      Interpretation:
       [min](x0, x1) = x0,
       
       [quot](x0, x1) = x0,
       
       [s](x0) = x0 + 1,
       
       [log](x0) = 0,
       
       [0] = 1,
       
       [log#](x0) = x0 + 1
      Strict:
       log# s s X -> log# s quot(X, s s 0())
       3 + 1X >= 2 + 1X
      Weak:
       
     Qed
   SCC (1):
    Strict:
     {quot#(s X, s Y) -> quot#(min(X, Y), s Y)}
    Weak:
    {   min(X, 0()) -> X,
      min(s X, s Y) -> min(X, Y),
     quot(0(), s Y) -> 0(),
     quot(s X, s Y) -> s quot(min(X, Y), s Y),
          log s 0() -> 0(),
          log s s X -> s log s quot(X, s s 0())}
    POLY:
     Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
     Interpretation:
      [min](x0, x1) = x0,
      
      [quot](x0, x1) = x0 + 1,
      
      [s](x0) = x0 + 1,
      
      [log](x0) = x0,
      
      [0] = 1,
      
      [quot#](x0, x1) = x0 + 1
     Strict:
      quot#(s X, s Y) -> quot#(min(X, Y), s Y)
      2 + 1X + 0Y >= 1 + 1X + 0Y
     Weak:
      
    Qed
   SCC (1):
    Strict:
     {min#(s X, s Y) -> min#(X, Y)}
    Weak:
    {   min(X, 0()) -> X,
      min(s X, s Y) -> min(X, Y),
     quot(0(), s Y) -> 0(),
     quot(s X, s Y) -> s quot(min(X, Y), s Y),
          log s 0() -> 0(),
          log s s X -> s log s quot(X, s s 0())}
    SPSC:
     Simple Projection:
      pi(min#) = 1
     Strict:
      {}
     Qed