Time: 5.135194
TRS:
 { Cond_eval_1(true(), x, y, z) -> eval_1(x, y, minus_int(x, y)),
            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_1(x, y, z) -> Cond_eval_1(and(and(greater_int(y, x), greater_int(z, y)), greater_int(y, pos 0())), x, y, z),
                eval_1(x, y, z) -> Cond_eval_11(and(and(greater_int(y, x), greater_int(z, y)), greater_int(y, pos 0())), x, y, z),
   Cond_eval_0(true(), x, y, z) -> eval_1(x, y, z),
         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),
  Cond_eval_11(true(), x, y, z) -> eval_1(plus_int(x, y), y, z),
        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),
                eval_0(x, y, z) -> Cond_eval_0(greater_int(y, pos 0()), x, y, z),
            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_eval_1(true(), x, y, z) -> eval_1(x, y, minus_int(x, y)),
              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_1(x, y, z) -> Cond_eval_1(and(and(greater_int(y, x), greater_int(z, y)), greater_int(y, pos 0())), x, y, z),
                  eval_1(x, y, z) -> Cond_eval_11(and(and(greater_int(y, x), greater_int(z, y)), greater_int(y, pos 0())), x, y, z),
     Cond_eval_0(true(), x, y, z) -> eval_1(x, y, z),
           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),
    Cond_eval_11(true(), x, y, z) -> eval_1(plus_int(x, y), y, z),
          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),
                  eval_0(x, y, z) -> Cond_eval_0(greater_int(y, pos 0()), x, y, z),
              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