Time: 5.074812
TRS:
 {                cd(true(), x) -> cd(greater_int(x, pos 0()), minus_int(x, pos s 0())),
  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),
        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),
            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),
               plus_nat(0(), x) -> x,
               plus_nat(s x, y) -> s plus_nat(x, y)}
 SRS: We consider a TRS.
  Trs:
   {                cd(true(), x) -> cd(greater_int(x, pos 0()), minus_int(x, pos s 0())),
    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),
          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),
              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),
                 plus_nat(0(), x) -> x,
                 plus_nat(s x, y) -> s plus_nat(x, y)}
  Fail