Time: 5.088230
TRS:
 {     Cond_eval1(true(), x, y) -> eval(minus_int(x, pos s 0()), x),
            and(true(), true()) -> true(),
           and(true(), false()) -> false(),
           and(false(), true()) -> false(),
          and(false(), false()) -> false(),
  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),
                     eval(x, y) -> Cond_eval1(and(greater_int(x, pos 0()), greater_int(y, pos 0())), x, y),
                     eval(x, y) -> Cond_eval(and(greater_int(x, pos 0()), greater_int(y, pos 0())), 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),
        Cond_eval(true(), x, y) -> eval(minus_int(y, pos s s 0()), plus_int(pos s 0(), x)),
         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(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:
   {     Cond_eval1(true(), x, y) -> eval(minus_int(x, pos s 0()), x),
              and(true(), true()) -> true(),
             and(true(), false()) -> false(),
             and(false(), true()) -> false(),
            and(false(), false()) -> false(),
    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),
                       eval(x, y) -> Cond_eval1(and(greater_int(x, pos 0()), greater_int(y, pos 0())), x, y),
                       eval(x, y) -> Cond_eval(and(greater_int(x, pos 0()), greater_int(y, pos 0())), 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),
          Cond_eval(true(), x, y) -> eval(minus_int(y, pos s s 0()), plus_int(pos s 0(), x)),
           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(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