Time: 5.025317
TRS:
 {         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(x, y) -> cond(greatereq_int(x, plus_int(pos s 0(), y)), x, y),
               cond(true(), x, y) -> plus_int(pos s 0(), minus(x, plus_int(pos s 0(), y))),
              cond(false(), x, y) -> pos 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(),
              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:
   {         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(x, y) -> cond(greatereq_int(x, plus_int(pos s 0(), y)), x, y),
                 cond(true(), x, y) -> plus_int(pos s 0(), minus(x, plus_int(pos s 0(), y))),
                cond(false(), x, y) -> pos 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(),
                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