Time: 5.091457
TRS:
 {      Cond_eval(true(), x, y) -> eval(plus_int(pos s 0(), x), plus_int(pos s s 0(), y)),
  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(x, y) -> Cond_eval(greater_int(x, y), x, y),
         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_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:
   {      Cond_eval(true(), x, y) -> eval(plus_int(pos s 0(), x), plus_int(pos s s 0(), y)),
    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(x, y) -> Cond_eval(greater_int(x, y), x, y),
           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_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