YES
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:
  Strict:
   {  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())))))}
  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()}
  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:
    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:
     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:
      Argument Filtering:
       pi(log#) = 0, pi(log) = [], pi(quot) = 0, pi(0) = [], pi(minus) = 0, pi(s) = [0], pi(pred) = 0
      Usable Rules:
       {}
      Interpretation:
       [s](x0) = x0 + 1
      Strict:
       {}
      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()}
      Qed
    SCC:
     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:
      Argument Filtering:
       pi(log) = [], pi(quot#) = 0, pi(quot) = [], pi(0) = [], pi(minus) = 0, pi(s) = [0], pi(pred) = 0
      Usable Rules:
       {}
      Interpretation:
       [s](x0) = x0 + 1
      Strict:
       {}
      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()}
      Qed
    SCC:
     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