Time: 5.015167
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, x) -> pos 0(),
                 minus(x, y) -> cond(min(x, y), x, y),
               cond(y, x, y) -> plus_int(pos s 0(), minus(x, plus_int(pos s 0(), y))),
           if(false(), u, v) -> v,
            if(true(), u, v) -> u,
  less_int(pos s x, pos s y) -> less_int(pos x, pos y),
  less_int(pos s x, pos 0()) -> false(),
  less_int(pos s x, neg s y) -> false(),
  less_int(pos s x, neg 0()) -> false(),
  less_int(pos 0(), pos s y) -> true(),
  less_int(pos 0(), pos 0()) -> false(),
  less_int(pos 0(), neg s y) -> false(),
  less_int(pos 0(), neg 0()) -> false(),
  less_int(neg s x, pos s y) -> true(),
  less_int(neg s x, pos 0()) -> true(),
  less_int(neg s x, neg s y) -> less_int(neg x, neg y),
  less_int(neg s x, neg 0()) -> true(),
  less_int(neg 0(), pos s y) -> true(),
  less_int(neg 0(), pos 0()) -> false(),
  less_int(neg 0(), neg s y) -> false(),
  less_int(neg 0(), neg 0()) -> false(),
                   min(u, v) -> if(less_int(u, v), u, v),
         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, x) -> pos 0(),
                   minus(x, y) -> cond(min(x, y), x, y),
                 cond(y, x, y) -> plus_int(pos s 0(), minus(x, plus_int(pos s 0(), y))),
             if(false(), u, v) -> v,
              if(true(), u, v) -> u,
    less_int(pos s x, pos s y) -> less_int(pos x, pos y),
    less_int(pos s x, pos 0()) -> false(),
    less_int(pos s x, neg s y) -> false(),
    less_int(pos s x, neg 0()) -> false(),
    less_int(pos 0(), pos s y) -> true(),
    less_int(pos 0(), pos 0()) -> false(),
    less_int(pos 0(), neg s y) -> false(),
    less_int(pos 0(), neg 0()) -> false(),
    less_int(neg s x, pos s y) -> true(),
    less_int(neg s x, pos 0()) -> true(),
    less_int(neg s x, neg s y) -> less_int(neg x, neg y),
    less_int(neg s x, neg 0()) -> true(),
    less_int(neg 0(), pos s y) -> true(),
    less_int(neg 0(), pos 0()) -> false(),
    less_int(neg 0(), neg s y) -> false(),
    less_int(neg 0(), neg 0()) -> false(),
                     min(u, v) -> if(less_int(u, v), u, v),
           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