abrutschen
to slip
To unintentionally lose one's grip or footing and slide downward.
Pass auf, der Pfad ist nass und man kann leicht abrutschen.
Be careful, the path is wet and you can easily slip.

to slip / to slide down
Loading your saved state.
to slip
To unintentionally lose one's grip or footing and slide downward.
Pass auf, der Pfad ist nass und man kann leicht abrutschen.
Be careful, the path is wet and you can easily slip.

'Abrutschen' is a separable verb. In a main clause, the prefix 'ab-' goes at the end of the sentence. In subordinate clauses or in the infinitive with 'zu', the verb stays together.
Vorsicht, der Hang rutscht bei Regen ab.
Careful, the slope slides down when it rains.
Since 'abrutschen' always describes a movement or a change of state, the perfect tense is formed with the auxiliary verb 'sein' (to be) in all meanings.
Ich bin auf der vereisten Treppe abgerutscht.
I slipped on the icy stairs.
The literal meaning of sliding downward is transferred to other areas. In a figurative sense, you can 'abrutschen' (slide) into a bad situation, poor performance, or a low social status.
Ohne Unterstützung der Familie wäre er vielleicht in die Kriminalität abgerutscht.
Without support from his family, he might have slid into crime.
When a decline is described, a preposition is often used to indicate the result. Typical are 'abrutschen auf' + accusative (for a rank) or 'abrutschen in' + accusative (for a state).
Der Verein ist auf den vorletzten Tabellenplatz abgerutscht.
The club has slipped to second-to-last place in the table.
When clothing or objects slip down from a person, that person is in the dative. The slipping item is the subject of the sentence.
Mir rutscht ständig die Hose.
My pants keep slipping down.
to fall / overthrow
'stürzen' and 'abrutschen' can both lead to an accident in which someone falls downward. But 'abrutschen' first describes the slipping: you lose your grip or footing and slide downward, for example on ice, on a slope, or from a ladder. 'stürzen' describes the fall itself more strongly and often the moment when someone lands on the ground. The words can be confused because 'abrutschen' often ends in a fall. If you want to emphasize the sliding movement, 'abrutschen' fits. If you want to emphasize the fall or accident, 'stürzen' fits.

Auf dem nassen Stein rutscht die Wanderin ab.
The hiker slips on the wet stone.
Am Abend stürzt er vor der Haustür und verletzt sich am Knie.
In the evening, he falls in front of the front door and injures his knee.