Time: 5.167827
TRS:
 {     Cond_eval_21(true(), x, y) -> eval_1(minus_int(x, pos s 0()), y),
              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),
    greater_int(pos 0(), pos 0()) -> false(),
    greater_int(pos 0(), pos s y) -> false(),
    greater_int(pos 0(), neg 0()) -> false(),
    greater_int(pos 0(), neg s y) -> true(),
    greater_int(pos s x, pos 0()) -> true(),
    greater_int(pos s x, pos s y) -> greater_int(pos x, pos y),
    greater_int(pos s x, neg 0()) -> true(),
    greater_int(pos s x, neg s y) -> true(),
    greater_int(neg 0(), pos 0()) -> false(),
    greater_int(neg 0(), pos s y) -> false(),
    greater_int(neg 0(), neg 0()) -> false(),
    greater_int(neg 0(), neg s y) -> true(),
    greater_int(neg s x, pos 0()) -> false(),
    greater_int(neg s x, pos s y) -> false(),
    greater_int(neg s x, neg 0()) -> false(),
    greater_int(neg s x, neg s y) -> greater_int(neg x, neg y),
                     eval_2(x, y) -> Cond_eval_21(and(and(greatereq_int(x, pos 0()), greater_int(y, pos 0())), greatereq_int(y, x)), x, y),
                     eval_2(x, y) -> Cond_eval_2(and(and(greatereq_int(x, pos 0()), greater_int(y, pos 0())), greater_int(x, y)), x, y),
        Cond_eval_2(true(), x, y) -> eval_2(x, mult_int(pos s s 0(), y)),
        Cond_eval_1(true(), x, y) -> eval_2(x, pos s 0()),
           mult_int(pos x, pos y) -> pos mult_nat(x, y),
           mult_int(pos x, neg y) -> neg mult_nat(x, y),
           mult_int(neg x, pos y) -> neg mult_nat(x, y),
           mult_int(neg x, neg y) -> pos mult_nat(x, y),
                     eval_1(x, y) -> Cond_eval_1(greatereq_int(x, pos 0()), x, 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),
                 mult_nat(0(), y) -> 0(),
               mult_nat(s x, 0()) -> 0(),
               mult_nat(s x, s y) -> plus_nat(mult_nat(x, s y), s y),
                 plus_nat(0(), x) -> x,
                 plus_nat(s x, y) -> s plus_nat(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)}
 SRS: We consider a TRS.
  Trs:
   {     Cond_eval_21(true(), x, y) -> eval_1(minus_int(x, pos s 0()), y),
                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),
      greater_int(pos 0(), pos 0()) -> false(),
      greater_int(pos 0(), pos s y) -> false(),
      greater_int(pos 0(), neg 0()) -> false(),
      greater_int(pos 0(), neg s y) -> true(),
      greater_int(pos s x, pos 0()) -> true(),
      greater_int(pos s x, pos s y) -> greater_int(pos x, pos y),
      greater_int(pos s x, neg 0()) -> true(),
      greater_int(pos s x, neg s y) -> true(),
      greater_int(neg 0(), pos 0()) -> false(),
      greater_int(neg 0(), pos s y) -> false(),
      greater_int(neg 0(), neg 0()) -> false(),
      greater_int(neg 0(), neg s y) -> true(),
      greater_int(neg s x, pos 0()) -> false(),
      greater_int(neg s x, pos s y) -> false(),
      greater_int(neg s x, neg 0()) -> false(),
      greater_int(neg s x, neg s y) -> greater_int(neg x, neg y),
                       eval_2(x, y) -> Cond_eval_21(and(and(greatereq_int(x, pos 0()), greater_int(y, pos 0())), greatereq_int(y, x)), x, y),
                       eval_2(x, y) -> Cond_eval_2(and(and(greatereq_int(x, pos 0()), greater_int(y, pos 0())), greater_int(x, y)), x, y),
          Cond_eval_2(true(), x, y) -> eval_2(x, mult_int(pos s s 0(), y)),
          Cond_eval_1(true(), x, y) -> eval_2(x, pos s 0()),
             mult_int(pos x, pos y) -> pos mult_nat(x, y),
             mult_int(pos x, neg y) -> neg mult_nat(x, y),
             mult_int(neg x, pos y) -> neg mult_nat(x, y),
             mult_int(neg x, neg y) -> pos mult_nat(x, y),
                       eval_1(x, y) -> Cond_eval_1(greatereq_int(x, pos 0()), x, 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),
                   mult_nat(0(), y) -> 0(),
                 mult_nat(s x, 0()) -> 0(),
                 mult_nat(s x, s y) -> plus_nat(mult_nat(x, s y), s y),
                   plus_nat(0(), x) -> x,
                   plus_nat(s x, y) -> s plus_nat(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)}
  Fail