Time: 5.180844
TRS:
 {                  f(x, z, u, w) -> Cond_f1(and(greatereq_int(x, w), greatereq_int(u, pos 0())), x, z, u, w),
                    f(x, z, u, w) -> Cond_f(greater_int(w, x), x, z, u, w),
           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),
      Cond_f1(true(), x, z, u, w) -> f(x, plus_int(pos s 0(), z), plus_int(pos s s 0(), u), plus_int(pos s s 0(), plus_int(w, u))),
       Cond_f(true(), x, z, u, w) -> z,
    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(),
                           sqrt x -> f(x, pos 0(), pos s 0(), pos s 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(),
              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}
 SRS: We consider a TRS.
  Trs:
   {                  f(x, z, u, w) -> Cond_f1(and(greatereq_int(x, w), greatereq_int(u, pos 0())), x, z, u, w),
                      f(x, z, u, w) -> Cond_f(greater_int(w, x), x, z, u, w),
             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),
        Cond_f1(true(), x, z, u, w) -> f(x, plus_int(pos s 0(), z), plus_int(pos s s 0(), u), plus_int(pos s s 0(), plus_int(w, u))),
         Cond_f(true(), x, z, u, w) -> z,
      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(),
                             sqrt x -> f(x, pos 0(), pos s 0(), pos s 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(),
                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}
  Fail