How does report and permanent ban system work?

So I played league ranked game after not playing for about 2~3 months, and I became little toxic and asked him why he didn't gank me when lane was pushed in. Instead of giving a good reason about it, he started to talk bad about me. Enemy members and my teammate Tristana started to talk bad about me too. I wans't toxic enough to get permanently get banned, but the others who talked bad about me were bad enough to get permanently banned. In the middle of the game, Lee Sin and Cait was saying "enjoy ur perma ba" I didn't know what they meant by that because there was no way I can get permanently banned by getting reported by more than 5 people in one ranked game, which I haven't played for a while, and I never got 14 days of suspension before if I am remembering it right . But somehow I did. I don't get how the system works. Can someone please explain to me how the system works? And are there any way I can know if others got banned? And plus, I don't have their messages, but enemy cait, graves, my team's lee, and Tristana was very toxic. I would like to know if they can get banned, and if any of them are members of League of Legends banning system or some sort. I don't think the system is really fair, and if possible, the fact that the members of the system of banning or some sort can simply just report you can get you permanently banned right after the game ended. Please, I asked you to give a me fair reason, fair rule, and a good explanation of how this can happen. Thank you.

P.s My ranked game ended about 5:32, 5/5/17. I got banned almost right away after the game ended, and plus, graves is in game right now; 5:42 5/5/17; even thought I reported him.

<removed by moderation> Game 1 Pure Thick: 쟂 Pure Thick: lucky ass boi Pure Thick: dont deserve that lvl 7 Pure Thick: my lane was pushed Pure Thick: no gank Pure Thick: nj Pure Thick: idk' Pure Thick: lee never ganks Pure Thick: that aint gank Pure Thick: just helpin Pure Thick: ur fault for not helpion when we coul've won lane Pure Thick: its urs when u could've helped in won the lane form e? Pure Thick: lmao' Pure Thick: i didnt even rage Pure Thick: and if i had no brain cells Pure Thick: how am i playin and talkin rn Pure Thick: how am i evne alive Pure Thick: buddy Pure Thick: sounds like u dont tho lee Pure Thick: cait Pure Thick: i feel like ur just fatass playin league all day Pure Thick: u may stfu Pure Thick: lmao' Pure Thick: says cait player Pure Thick: ironic Pure Thick: didknt know yas players were all fatasses Pure Thick: u like that lee? Pure Thick: hye lee Pure Thick: i just won 2v1 at top Pure Thick: u like it? Pure Thick: than how did u not get me graves Pure Thick: lmao Pure Thick: ty Pure Thick: So r u buddy Pure Thick: u r too budyd Pure Thick: no one gives fk about u too cait Pure Thick: i dont need a %%% like u' Pure Thick: i alreay got many freinds Pure Thick: Damn Pure Thick: so many %%%s in plat now Pure Thick: season 6 was way better smgh Pure Thick: perma ban for what? Pure Thick: talkin shit? Pure Thick: looks like u guys were too Pure Thick: idk dude Pure Thick: same Pure Thick: whos smurf Pure Thick: trist Pure Thick: ur just bad Pure Thick: u lost eral Pure Thick: u lost eraly too