Time: 5.114122
TRS:
 {    Cond_eval1(true(), x, y, z) -> eval(minus_int(x, z), plus_int(y, mult_int(z, z)), minus_int(z, pos s 0())),
    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(),
                    eval(x, y, z) -> Cond_eval1(greatereq_int(x, y), x, y, z),
                    eval(x, y, z) -> Cond_eval(greatereq_int(x, y), x, y, z),
       Cond_eval(true(), x, y, z) -> eval(plus_int(pos s 0(), x), plus_int(y, x), 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),
          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_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),
              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,
               mult_nat(s x, s y) -> plus_nat(mult_nat(x, s y), s y),
               mult_nat(s x, 0()) -> 0(),
                 mult_nat(0(), y) -> 0()}
 SRS: We consider a TRS.
  Trs:
   {    Cond_eval1(true(), x, y, z) -> eval(minus_int(x, z), plus_int(y, mult_int(z, z)), minus_int(z, pos s 0())),
      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(),
                      eval(x, y, z) -> Cond_eval1(greatereq_int(x, y), x, y, z),
                      eval(x, y, z) -> Cond_eval(greatereq_int(x, y), x, y, z),
         Cond_eval(true(), x, y, z) -> eval(plus_int(pos s 0(), x), plus_int(y, x), 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),
            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_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),
                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,
                 mult_nat(s x, s y) -> plus_nat(mult_nat(x, s y), s y),
                 mult_nat(s x, 0()) -> 0(),
                   mult_nat(0(), y) -> 0()}
  Fail