Time: 5.248409
TRS:
 {                eval_2(x, y, z) -> Cond_eval_21(greater_int(y, z), x, y, z),
                  eval_2(x, y, z) -> Cond_eval_2(greatereq_int(z, y), x, y, z),
     Cond_eval_1(true(), x, y, z) -> eval_2(x, y, z),
              and(true(), true()) -> true(),
             and(true(), false()) -> false(),
             and(false(), true()) -> false(),
            and(false(), false()) -> false(),
      equal_int(pos s x, pos s y) -> equal_int(pos x, pos y),
      equal_int(pos s x, pos 0()) -> false(),
      equal_int(pos s x, neg s y) -> false(),
      equal_int(pos s x, neg 0()) -> false(),
      equal_int(pos 0(), pos s y) -> false(),
      equal_int(pos 0(), pos 0()) -> true(),
      equal_int(pos 0(), neg s y) -> false(),
      equal_int(pos 0(), neg 0()) -> true(),
      equal_int(neg s x, pos s y) -> false(),
      equal_int(neg s x, pos 0()) -> false(),
      equal_int(neg s x, neg s y) -> equal_int(neg x, neg y),
      equal_int(neg s x, neg 0()) -> false(),
      equal_int(neg 0(), pos s y) -> false(),
      equal_int(neg 0(), pos 0()) -> true(),
      equal_int(neg 0(), neg s y) -> false(),
      equal_int(neg 0(), neg 0()) -> 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(),
                  eval_1(x, y, z) -> Cond_eval_1(and(equal_int(x, y), greater_int(x, z)), x, y, z),
    Cond_eval_21(true(), x, y, z) -> eval_2(minus_int(x, pos s 0()), minus_int(y, pos s 0()), z),
          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),
     Cond_eval_2(true(), x, y, z) -> eval_1(x, y, z),
    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:
   {                eval_2(x, y, z) -> Cond_eval_21(greater_int(y, z), x, y, z),
                    eval_2(x, y, z) -> Cond_eval_2(greatereq_int(z, y), x, y, z),
       Cond_eval_1(true(), x, y, z) -> eval_2(x, y, z),
                and(true(), true()) -> true(),
               and(true(), false()) -> false(),
               and(false(), true()) -> false(),
              and(false(), false()) -> false(),
        equal_int(pos s x, pos s y) -> equal_int(pos x, pos y),
        equal_int(pos s x, pos 0()) -> false(),
        equal_int(pos s x, neg s y) -> false(),
        equal_int(pos s x, neg 0()) -> false(),
        equal_int(pos 0(), pos s y) -> false(),
        equal_int(pos 0(), pos 0()) -> true(),
        equal_int(pos 0(), neg s y) -> false(),
        equal_int(pos 0(), neg 0()) -> true(),
        equal_int(neg s x, pos s y) -> false(),
        equal_int(neg s x, pos 0()) -> false(),
        equal_int(neg s x, neg s y) -> equal_int(neg x, neg y),
        equal_int(neg s x, neg 0()) -> false(),
        equal_int(neg 0(), pos s y) -> false(),
        equal_int(neg 0(), pos 0()) -> true(),
        equal_int(neg 0(), neg s y) -> false(),
        equal_int(neg 0(), neg 0()) -> 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(),
                    eval_1(x, y, z) -> Cond_eval_1(and(equal_int(x, y), greater_int(x, z)), x, y, z),
      Cond_eval_21(true(), x, y, z) -> eval_2(minus_int(x, pos s 0()), minus_int(y, pos s 0()), z),
            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),
       Cond_eval_2(true(), x, y, z) -> eval_1(x, y, z),
      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