Time: 5.174249
TRS:
{ Cond_eval1(true(), x, y, z) -> eval(x, minus_int(y, pos s 0()), plus_int(z, y)),
and(true(), true()) -> true(),
and(true(), false()) -> false(),
and(false(), true()) -> false(),
and(false(), false()) -> false(),
greatereq_int(pos x, pos 0()) -> true(),
greatereq_int(pos x, neg y) -> true(),
greatereq_int(pos 0(), pos s y) -> false(),
greatereq_int(pos s x, pos s y) -> greatereq_int(pos x, pos y),
greatereq_int(neg x, pos s y) -> false(),
greatereq_int(neg 0(), pos 0()) -> true(),
greatereq_int(neg 0(), neg y) -> true(),
greatereq_int(neg s x, pos 0()) -> false(),
greatereq_int(neg s x, neg 0()) -> false(),
greatereq_int(neg s x, neg s y) -> greatereq_int(neg x, neg y),
mult_int(pos x, pos y) -> pos mult_nat(x, y),
mult_int(pos x, neg y) -> neg mult_nat(x, y),
mult_int(neg x, pos y) -> neg mult_nat(x, y),
mult_int(neg x, neg y) -> pos mult_nat(x, y),
eval(x, y, z) -> Cond_eval1(and(greatereq_int(x, pos 0()), greatereq_int(mult_int(mult_int(z, z), z), y)), x, y, z),
eval(x, y, z) -> Cond_eval(and(greatereq_int(x, pos 0()), greatereq_int(mult_int(mult_int(z, z), z), y)), x, 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),
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(true(), x, y, z) -> eval(minus_int(x, pos s 0()), minus_int(y, pos s 0()), z),
mult_nat(0(), y) -> 0(),
mult_nat(s x, 0()) -> 0(),
mult_nat(s x, s y) -> plus_nat(mult_nat(x, s y), s y),
plus_nat(0(), x) -> x,
plus_nat(s x, y) -> s 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)}
SRS: We consider a TRS.
Trs:
{ Cond_eval1(true(), x, y, z) -> eval(x, minus_int(y, pos s 0()), plus_int(z, y)),
and(true(), true()) -> true(),
and(true(), false()) -> false(),
and(false(), true()) -> false(),
and(false(), false()) -> false(),
greatereq_int(pos x, pos 0()) -> true(),
greatereq_int(pos x, neg y) -> true(),
greatereq_int(pos 0(), pos s y) -> false(),
greatereq_int(pos s x, pos s y) -> greatereq_int(pos x, pos y),
greatereq_int(neg x, pos s y) -> false(),
greatereq_int(neg 0(), pos 0()) -> true(),
greatereq_int(neg 0(), neg y) -> true(),
greatereq_int(neg s x, pos 0()) -> false(),
greatereq_int(neg s x, neg 0()) -> false(),
greatereq_int(neg s x, neg s y) -> greatereq_int(neg x, neg y),
mult_int(pos x, pos y) -> pos mult_nat(x, y),
mult_int(pos x, neg y) -> neg mult_nat(x, y),
mult_int(neg x, pos y) -> neg mult_nat(x, y),
mult_int(neg x, neg y) -> pos mult_nat(x, y),
eval(x, y, z) -> Cond_eval1(and(greatereq_int(x, pos 0()), greatereq_int(mult_int(mult_int(z, z), z), y)), x, y, z),
eval(x, y, z) -> Cond_eval(and(greatereq_int(x, pos 0()), greatereq_int(mult_int(mult_int(z, z), z), y)), x, 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),
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(true(), x, y, z) -> eval(minus_int(x, pos s 0()), minus_int(y, pos s 0()), z),
mult_nat(0(), y) -> 0(),
mult_nat(s x, 0()) -> 0(),
mult_nat(s x, s y) -> plus_nat(mult_nat(x, s y), s y),
plus_nat(0(), x) -> x,
plus_nat(s x, y) -> s 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)}
Fail