Time: 5.138738 TRS: { cu(true(), x) -> cu(less_int(x, exp(pos s s s s s s s s s s 0(), pos s s 0())), plus_int(pos s 0(), x)), less_int(pos s x, pos s y) -> less_int(pos x, pos y), less_int(pos s x, pos 0()) -> false(), less_int(pos s x, neg s y) -> false(), less_int(pos s x, neg 0()) -> false(), less_int(pos 0(), pos s y) -> true(), less_int(pos 0(), pos 0()) -> false(), less_int(pos 0(), neg s y) -> false(), less_int(pos 0(), neg 0()) -> false(), less_int(neg s x, pos s y) -> true(), less_int(neg s x, pos 0()) -> true(), less_int(neg s x, neg s y) -> less_int(neg x, neg y), less_int(neg s x, neg 0()) -> true(), less_int(neg 0(), pos s y) -> true(), less_int(neg 0(), pos 0()) -> false(), less_int(neg 0(), neg s y) -> false(), less_int(neg 0(), neg 0()) -> false(), exp(x, y) -> if(greater_int(y, pos 0()), 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), if(true(), x, y) -> mult_int(x, exp(x, minus_int(y, pos s 0()))), if(false(), x, y) -> pos s 0(), 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(), 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), 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(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, mult_nat(s x, s y) -> plus_nat(mult_nat(x, s y), s y), mult_nat(s x, 0()) -> 0(), mult_nat(0(), y) -> 0()} SRS: We consider a TRS. Trs: { cu(true(), x) -> cu(less_int(x, exp(pos s s s s s s s s s s 0(), pos s s 0())), plus_int(pos s 0(), x)), less_int(pos s x, pos s y) -> less_int(pos x, pos y), less_int(pos s x, pos 0()) -> false(), less_int(pos s x, neg s y) -> false(), less_int(pos s x, neg 0()) -> false(), less_int(pos 0(), pos s y) -> true(), less_int(pos 0(), pos 0()) -> false(), less_int(pos 0(), neg s y) -> false(), less_int(pos 0(), neg 0()) -> false(), less_int(neg s x, pos s y) -> true(), less_int(neg s x, pos 0()) -> true(), less_int(neg s x, neg s y) -> less_int(neg x, neg y), less_int(neg s x, neg 0()) -> true(), less_int(neg 0(), pos s y) -> true(), less_int(neg 0(), pos 0()) -> false(), less_int(neg 0(), neg s y) -> false(), less_int(neg 0(), neg 0()) -> false(), exp(x, y) -> if(greater_int(y, pos 0()), 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), if(true(), x, y) -> mult_int(x, exp(x, minus_int(y, pos s 0()))), if(false(), x, y) -> pos s 0(), 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(), 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), 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(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, mult_nat(s x, s y) -> plus_nat(mult_nat(x, s y), s y), mult_nat(s x, 0()) -> 0(), mult_nat(0(), y) -> 0()} Fail