MAYBE
TRS:
 {          half(0()) -> 0(),
         half(s(0())) -> 0(),
        half(s(s(x))) -> s(half(x)),
           le(0(), y) -> true(),
        le(s(x), 0()) -> false(),
       le(s(x), s(y)) -> le(x, y),
             inc(0()) -> 0(),
            inc(s(x)) -> s(inc(x)),
           log2(x, y) -> if(le(x, s(0())), x, inc(y)),
               log(x) -> log2(x, 0()),
  if(true(), x, s(y)) -> y,
    if(false(), x, y) -> log2(half(x), y)}
 DP:
  Strict:
   {    half#(s(s(x))) -> half#(x),
       le#(s(x), s(y)) -> le#(x, y),
            inc#(s(x)) -> inc#(x),
           log2#(x, y) -> le#(x, s(0())),
           log2#(x, y) -> inc#(y),
           log2#(x, y) -> if#(le(x, s(0())), x, inc(y)),
               log#(x) -> log2#(x, 0()),
    if#(false(), x, y) -> half#(x),
    if#(false(), x, y) -> log2#(half(x), y)}
  Weak:
  {          half(0()) -> 0(),
          half(s(0())) -> 0(),
         half(s(s(x))) -> s(half(x)),
            le(0(), y) -> true(),
         le(s(x), 0()) -> false(),
        le(s(x), s(y)) -> le(x, y),
              inc(0()) -> 0(),
             inc(s(x)) -> s(inc(x)),
            log2(x, y) -> if(le(x, s(0())), x, inc(y)),
                log(x) -> log2(x, 0()),
   if(true(), x, s(y)) -> y,
     if(false(), x, y) -> log2(half(x), y)}
  EDG:
   {(log2#(x, y) -> inc#(y), inc#(s(x)) -> inc#(x))
    (le#(s(x), s(y)) -> le#(x, y), le#(s(x), s(y)) -> le#(x, y))
    (inc#(s(x)) -> inc#(x), inc#(s(x)) -> inc#(x))
    (if#(false(), x, y) -> half#(x), half#(s(s(x))) -> half#(x))
    (log2#(x, y) -> if#(le(x, s(0())), x, inc(y)), if#(false(), x, y) -> half#(x))
    (log2#(x, y) -> if#(le(x, s(0())), x, inc(y)), if#(false(), x, y) -> log2#(half(x), y))
    (log2#(x, y) -> le#(x, s(0())), le#(s(x), s(y)) -> le#(x, y))
    (half#(s(s(x))) -> half#(x), half#(s(s(x))) -> half#(x))
    (if#(false(), x, y) -> log2#(half(x), y), log2#(x, y) -> le#(x, s(0())))
    (if#(false(), x, y) -> log2#(half(x), y), log2#(x, y) -> inc#(y))
    (if#(false(), x, y) -> log2#(half(x), y), log2#(x, y) -> if#(le(x, s(0())), x, inc(y)))
    (log#(x) -> log2#(x, 0()), log2#(x, y) -> le#(x, s(0())))
    (log#(x) -> log2#(x, 0()), log2#(x, y) -> inc#(y))
    (log#(x) -> log2#(x, 0()), log2#(x, y) -> if#(le(x, s(0())), x, inc(y)))}
   SCCS:
    Scc:
     {       log2#(x, y) -> if#(le(x, s(0())), x, inc(y)),
      if#(false(), x, y) -> log2#(half(x), y)}
    Scc:
     {inc#(s(x)) -> inc#(x)}
    Scc:
     {le#(s(x), s(y)) -> le#(x, y)}
    Scc:
     {half#(s(s(x))) -> half#(x)}
    SCC:
     Strict:
      {       log2#(x, y) -> if#(le(x, s(0())), x, inc(y)),
       if#(false(), x, y) -> log2#(half(x), y)}
     Weak:
     {          half(0()) -> 0(),
             half(s(0())) -> 0(),
            half(s(s(x))) -> s(half(x)),
               le(0(), y) -> true(),
            le(s(x), 0()) -> false(),
           le(s(x), s(y)) -> le(x, y),
                 inc(0()) -> 0(),
                inc(s(x)) -> s(inc(x)),
               log2(x, y) -> if(le(x, s(0())), x, inc(y)),
                   log(x) -> log2(x, 0()),
      if(true(), x, s(y)) -> y,
        if(false(), x, y) -> log2(half(x), y)}
     Fail
    SCC:
     Strict:
      {inc#(s(x)) -> inc#(x)}
     Weak:
     {          half(0()) -> 0(),
             half(s(0())) -> 0(),
            half(s(s(x))) -> s(half(x)),
               le(0(), y) -> true(),
            le(s(x), 0()) -> false(),
           le(s(x), s(y)) -> le(x, y),
                 inc(0()) -> 0(),
                inc(s(x)) -> s(inc(x)),
               log2(x, y) -> if(le(x, s(0())), x, inc(y)),
                   log(x) -> log2(x, 0()),
      if(true(), x, s(y)) -> y,
        if(false(), x, y) -> log2(half(x), y)}
     SPSC:
      Simple Projection:
       pi(inc#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {le#(s(x), s(y)) -> le#(x, y)}
     Weak:
     {          half(0()) -> 0(),
             half(s(0())) -> 0(),
            half(s(s(x))) -> s(half(x)),
               le(0(), y) -> true(),
            le(s(x), 0()) -> false(),
           le(s(x), s(y)) -> le(x, y),
                 inc(0()) -> 0(),
                inc(s(x)) -> s(inc(x)),
               log2(x, y) -> if(le(x, s(0())), x, inc(y)),
                   log(x) -> log2(x, 0()),
      if(true(), x, s(y)) -> y,
        if(false(), x, y) -> log2(half(x), y)}
     SPSC:
      Simple Projection:
       pi(le#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {half#(s(s(x))) -> half#(x)}
     Weak:
     {          half(0()) -> 0(),
             half(s(0())) -> 0(),
            half(s(s(x))) -> s(half(x)),
               le(0(), y) -> true(),
            le(s(x), 0()) -> false(),
           le(s(x), s(y)) -> le(x, y),
                 inc(0()) -> 0(),
                inc(s(x)) -> s(inc(x)),
               log2(x, y) -> if(le(x, s(0())), x, inc(y)),
                   log(x) -> log2(x, 0()),
      if(true(), x, s(y)) -> y,
        if(false(), x, y) -> log2(half(x), y)}
     SPSC:
      Simple Projection:
       pi(half#) = 0
      Strict:
       {}
      Qed