Consider the TRS R consisting of the rewrite rules

1: quot(0,s(y),s(z)) -> 0
2: quot(s(x),s(y),z) -> quot(x,y,z)
3: quot(x,0,s(z)) -> s(quot(x,s(z),s(z)))

There are 2 dependency pairs:

4: QUOT(s(x),s(y),z) -> QUOT(x,y,z)
5: QUOT(x,0,s(z)) -> QUOT(x,s(z),s(z))

The approximated dependency graph contains one SCC:
{4,5}.

- Consider the SCC {4,5}.
There are no usable rules.
By taking the polynomial interpretation
[0] = 1,
[s](x) = x + 1
and [QUOT](x,y,z) = x + z + 1,
rule 5
is weakly decreasing and
rule 4
is strictly decreasing.

Hence the TRS is terminating.