Time: 5.152203
TRS:
 {                     d(x, y, z) -> dNat(and(and(greatereq_int(x, pos 0()), greatereq_int(y, pos s 0())), greatereq_int(z, pos 0())), x, y, z),
             divNat(true(), x, y) -> d(x, y, pos 0()),
            cond(true(), x, y, z) -> plus_int(pos s 0(), d(x, plus_int(pos s 0(), y), plus_int(plus_int(pos s 0(), y), z))),
           cond(false(), x, y, z) -> pos 0(),
    greatereq_int(pos x, pos 0()) -> true(),
      greatereq_int(pos x, neg y) -> true(),
  greatereq_int(pos 0(), pos s y) -> false(),
  greatereq_int(pos s x, pos s y) -> greatereq_int(pos x, pos y),
    greatereq_int(neg x, pos s y) -> false(),
  greatereq_int(neg 0(), pos 0()) -> true(),
    greatereq_int(neg 0(), neg y) -> true(),
  greatereq_int(neg s x, pos 0()) -> false(),
  greatereq_int(neg s x, neg 0()) -> false(),
  greatereq_int(neg s x, neg s y) -> greatereq_int(neg x, neg y),
          minus_int(pos x, pos y) -> minus_nat(x, y),
          minus_int(pos x, neg y) -> pos plus_nat(x, y),
          minus_int(neg x, pos y) -> neg plus_nat(x, y),
          minus_int(neg x, neg y) -> minus_nat(y, x),
            dNat(true(), x, y, z) -> cond(greatereq_int(x, z), x, minus_int(y, pos s 0()), z),
           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),
              and(true(), true()) -> true(),
             and(true(), false()) -> false(),
             and(false(), true()) -> false(),
            and(false(), false()) -> false(),
                        div(x, y) -> divNat(and(greatereq_int(x, pos 0()), greatereq_int(y, pos s 0())), x, y),
              minus_nat(0(), 0()) -> pos 0(),
              minus_nat(0(), s y) -> neg s y,
              minus_nat(s x, 0()) -> pos s x,
              minus_nat(s x, s y) -> minus_nat(x, y),
                 plus_nat(0(), x) -> x,
                 plus_nat(s x, y) -> s plus_nat(x, y)}
 SRS: We consider a TRS.
  Trs:
   {                     d(x, y, z) -> dNat(and(and(greatereq_int(x, pos 0()), greatereq_int(y, pos s 0())), greatereq_int(z, pos 0())), x, y, z),
               divNat(true(), x, y) -> d(x, y, pos 0()),
              cond(true(), x, y, z) -> plus_int(pos s 0(), d(x, plus_int(pos s 0(), y), plus_int(plus_int(pos s 0(), y), z))),
             cond(false(), x, y, z) -> pos 0(),
      greatereq_int(pos x, pos 0()) -> true(),
        greatereq_int(pos x, neg y) -> true(),
    greatereq_int(pos 0(), pos s y) -> false(),
    greatereq_int(pos s x, pos s y) -> greatereq_int(pos x, pos y),
      greatereq_int(neg x, pos s y) -> false(),
    greatereq_int(neg 0(), pos 0()) -> true(),
      greatereq_int(neg 0(), neg y) -> true(),
    greatereq_int(neg s x, pos 0()) -> false(),
    greatereq_int(neg s x, neg 0()) -> false(),
    greatereq_int(neg s x, neg s y) -> greatereq_int(neg x, neg y),
            minus_int(pos x, pos y) -> minus_nat(x, y),
            minus_int(pos x, neg y) -> pos plus_nat(x, y),
            minus_int(neg x, pos y) -> neg plus_nat(x, y),
            minus_int(neg x, neg y) -> minus_nat(y, x),
              dNat(true(), x, y, z) -> cond(greatereq_int(x, z), x, minus_int(y, pos s 0()), z),
             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),
                and(true(), true()) -> true(),
               and(true(), false()) -> false(),
               and(false(), true()) -> false(),
              and(false(), false()) -> false(),
                          div(x, y) -> divNat(and(greatereq_int(x, pos 0()), greatereq_int(y, pos s 0())), x, y),
                minus_nat(0(), 0()) -> pos 0(),
                minus_nat(0(), s y) -> neg s y,
                minus_nat(s x, 0()) -> pos s x,
                minus_nat(s x, s y) -> minus_nat(x, y),
                   plus_nat(0(), x) -> x,
                   plus_nat(s x, y) -> s plus_nat(x, y)}
  Fail