Time: 5.137275
TRS:
 {        Cond_eval(true(), l, u) -> eval(l, div_int(plus_int(l, u), pos s 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 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),
       less_int(pos 0(), pos 0()) -> false(),
       less_int(pos 0(), pos s y) -> true(),
       less_int(pos 0(), neg 0()) -> false(),
       less_int(pos 0(), neg s y) -> false(),
       less_int(pos s x, pos 0()) -> false(),
       less_int(pos s x, pos s y) -> less_int(pos x, pos y),
       less_int(pos s x, neg 0()) -> false(),
       less_int(pos s x, neg s y) -> false(),
       less_int(neg 0(), pos 0()) -> false(),
       less_int(neg 0(), pos s y) -> true(),
       less_int(neg 0(), neg 0()) -> false(),
       less_int(neg 0(), neg s y) -> false(),
       less_int(neg s x, pos 0()) -> true(),
       less_int(neg s x, pos s y) -> true(),
       less_int(neg s x, neg 0()) -> true(),
       less_int(neg s x, neg s y) -> less_int(neg x, neg y),
                       eval(l, u) -> Cond_eval(and(and(greatereq_int(l, pos 0()), greatereq_int(u, pos 0())), less_int(l, u)), l, u),
                       eval(l, u) -> Cond_eval1(and(and(greatereq_int(l, pos 0()), greatereq_int(u, pos 0())), less_int(l, u)), l, u),
           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),
          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),
         Cond_eval1(true(), l, u) -> eval(plus_int(pos s 0(), div_int(plus_int(l, u), pos s s 0())), u),
              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),
                div_nat(0(), s y) -> 0(),
                div_nat(s x, s y) -> if(greatereq_int(pos x, pos y), div_nat(minus_nat_s(x, y), s y), 0()),
                 if(true(), x, y) -> x,
                if(false(), x, y) -> y,
              minus_nat_s(x, 0()) -> x,
            minus_nat_s(0(), s y) -> 0(),
            minus_nat_s(s x, s y) -> minus_nat_s(x, y)}
 SRS: We consider a TRS.
  Trs:
   {        Cond_eval(true(), l, u) -> eval(l, div_int(plus_int(l, u), pos s 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 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),
         less_int(pos 0(), pos 0()) -> false(),
         less_int(pos 0(), pos s y) -> true(),
         less_int(pos 0(), neg 0()) -> false(),
         less_int(pos 0(), neg s y) -> false(),
         less_int(pos s x, pos 0()) -> false(),
         less_int(pos s x, pos s y) -> less_int(pos x, pos y),
         less_int(pos s x, neg 0()) -> false(),
         less_int(pos s x, neg s y) -> false(),
         less_int(neg 0(), pos 0()) -> false(),
         less_int(neg 0(), pos s y) -> true(),
         less_int(neg 0(), neg 0()) -> false(),
         less_int(neg 0(), neg s y) -> false(),
         less_int(neg s x, pos 0()) -> true(),
         less_int(neg s x, pos s y) -> true(),
         less_int(neg s x, neg 0()) -> true(),
         less_int(neg s x, neg s y) -> less_int(neg x, neg y),
                         eval(l, u) -> Cond_eval(and(and(greatereq_int(l, pos 0()), greatereq_int(u, pos 0())), less_int(l, u)), l, u),
                         eval(l, u) -> Cond_eval1(and(and(greatereq_int(l, pos 0()), greatereq_int(u, pos 0())), less_int(l, u)), l, u),
             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),
            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),
           Cond_eval1(true(), l, u) -> eval(plus_int(pos s 0(), div_int(plus_int(l, u), pos s s 0())), u),
                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),
                  div_nat(0(), s y) -> 0(),
                  div_nat(s x, s y) -> if(greatereq_int(pos x, pos y), div_nat(minus_nat_s(x, y), s y), 0()),
                   if(true(), x, y) -> x,
                  if(false(), x, y) -> y,
                minus_nat_s(x, 0()) -> x,
              minus_nat_s(0(), s y) -> 0(),
              minus_nat_s(s x, s y) -> minus_nat_s(x, y)}
  Fail