Time: 5.150773
TRS:
 {         plus_int(pos x, pos y) -> pos plus_nat(x, y),
           plus_int(pos x, neg y) -> minus_nat(x, y),
           plus_int(neg x, pos y) -> minus_nat(y, x),
           plus_int(neg x, neg y) -> neg plus_nat(x, y),
                        log(x, y) -> lif(and(greatereq_int(x, y), greater_int(y, pos s 0())), x, y),
          div_int(pos x, pos s y) -> pos div_nat(x, s y),
          div_int(pos x, neg s y) -> neg div_nat(x, s y),
          div_int(neg x, pos s y) -> neg div_nat(x, s y),
          div_int(neg x, neg s y) -> pos div_nat(x, s y),
                lif(true(), x, y) -> plus_int(pos s 0(), log(div_int(x, y), y)),
               lif(false(), x, y) -> pos 0(),
              and(true(), true()) -> true(),
             and(true(), false()) -> false(),
             and(false(), true()) -> false(),
            and(false(), false()) -> false(),
    greatereq_int(pos x, pos 0()) -> true(),
      greatereq_int(pos x, neg y) -> true(),
  greatereq_int(pos s x, pos s y) -> greatereq_int(pos x, pos y),
  greatereq_int(pos 0(), pos s y) -> false(),
    greatereq_int(neg x, pos s y) -> false(),
  greatereq_int(neg s x, pos 0()) -> false(),
  greatereq_int(neg s x, neg s y) -> greatereq_int(neg x, neg y),
  greatereq_int(neg s x, neg 0()) -> false(),
  greatereq_int(neg 0(), pos 0()) -> true(),
    greatereq_int(neg 0(), neg y) -> true(),
    greater_int(pos s x, pos s y) -> greater_int(pos x, pos y),
    greater_int(pos s x, pos 0()) -> true(),
    greater_int(pos s x, neg s y) -> true(),
    greater_int(pos s x, neg 0()) -> true(),
    greater_int(pos 0(), pos s y) -> false(),
    greater_int(pos 0(), pos 0()) -> false(),
    greater_int(pos 0(), neg s y) -> true(),
    greater_int(pos 0(), neg 0()) -> false(),
    greater_int(neg s x, pos s y) -> false(),
    greater_int(neg s x, pos 0()) -> false(),
    greater_int(neg s x, neg s y) -> greater_int(neg x, neg y),
    greater_int(neg s x, neg 0()) -> false(),
    greater_int(neg 0(), pos s y) -> false(),
    greater_int(neg 0(), pos 0()) -> false(),
    greater_int(neg 0(), neg s y) -> true(),
    greater_int(neg 0(), neg 0()) -> false(),
              minus_nat(s x, s y) -> minus_nat(x, y),
              minus_nat(s x, 0()) -> pos s x,
              minus_nat(0(), s y) -> neg s y,
              minus_nat(0(), 0()) -> pos 0(),
                 plus_nat(s x, y) -> s plus_nat(x, y),
                 plus_nat(0(), x) -> x,
                div_nat(s x, s y) -> if(greatereq_int(pos x, pos y), div_nat(minus_nat_s(x, y), s y), 0()),
                div_nat(0(), s y) -> 0(),
                 if(true(), x, y) -> x,
                if(false(), x, y) -> y,
              minus_nat_s(x, 0()) -> x,
            minus_nat_s(s x, s y) -> minus_nat_s(x, y),
            minus_nat_s(0(), s y) -> 0()}
 SRS: We consider a TRS.
  Trs:
   {         plus_int(pos x, pos y) -> pos plus_nat(x, y),
             plus_int(pos x, neg y) -> minus_nat(x, y),
             plus_int(neg x, pos y) -> minus_nat(y, x),
             plus_int(neg x, neg y) -> neg plus_nat(x, y),
                          log(x, y) -> lif(and(greatereq_int(x, y), greater_int(y, pos s 0())), x, y),
            div_int(pos x, pos s y) -> pos div_nat(x, s y),
            div_int(pos x, neg s y) -> neg div_nat(x, s y),
            div_int(neg x, pos s y) -> neg div_nat(x, s y),
            div_int(neg x, neg s y) -> pos div_nat(x, s y),
                  lif(true(), x, y) -> plus_int(pos s 0(), log(div_int(x, y), y)),
                 lif(false(), x, y) -> pos 0(),
                and(true(), true()) -> true(),
               and(true(), false()) -> false(),
               and(false(), true()) -> false(),
              and(false(), false()) -> false(),
      greatereq_int(pos x, pos 0()) -> true(),
        greatereq_int(pos x, neg y) -> true(),
    greatereq_int(pos s x, pos s y) -> greatereq_int(pos x, pos y),
    greatereq_int(pos 0(), pos s y) -> false(),
      greatereq_int(neg x, pos s y) -> false(),
    greatereq_int(neg s x, pos 0()) -> false(),
    greatereq_int(neg s x, neg s y) -> greatereq_int(neg x, neg y),
    greatereq_int(neg s x, neg 0()) -> false(),
    greatereq_int(neg 0(), pos 0()) -> true(),
      greatereq_int(neg 0(), neg y) -> true(),
      greater_int(pos s x, pos s y) -> greater_int(pos x, pos y),
      greater_int(pos s x, pos 0()) -> true(),
      greater_int(pos s x, neg s y) -> true(),
      greater_int(pos s x, neg 0()) -> true(),
      greater_int(pos 0(), pos s y) -> false(),
      greater_int(pos 0(), pos 0()) -> false(),
      greater_int(pos 0(), neg s y) -> true(),
      greater_int(pos 0(), neg 0()) -> false(),
      greater_int(neg s x, pos s y) -> false(),
      greater_int(neg s x, pos 0()) -> false(),
      greater_int(neg s x, neg s y) -> greater_int(neg x, neg y),
      greater_int(neg s x, neg 0()) -> false(),
      greater_int(neg 0(), pos s y) -> false(),
      greater_int(neg 0(), pos 0()) -> false(),
      greater_int(neg 0(), neg s y) -> true(),
      greater_int(neg 0(), neg 0()) -> false(),
                minus_nat(s x, s y) -> minus_nat(x, y),
                minus_nat(s x, 0()) -> pos s x,
                minus_nat(0(), s y) -> neg s y,
                minus_nat(0(), 0()) -> pos 0(),
                   plus_nat(s x, y) -> s plus_nat(x, y),
                   plus_nat(0(), x) -> x,
                  div_nat(s x, s y) -> if(greatereq_int(pos x, pos y), div_nat(minus_nat_s(x, y), s y), 0()),
                  div_nat(0(), s y) -> 0(),
                   if(true(), x, y) -> x,
                  if(false(), x, y) -> y,
                minus_nat_s(x, 0()) -> x,
              minus_nat_s(s x, s y) -> minus_nat_s(x, y),
              minus_nat_s(0(), s y) -> 0()}
  Fail