Consider the TRS R consisting of the rewrite rules

1: x  x -> e
2: x / x -> e
3: e . x -> x
4: x . e -> x
5: e  x -> x
6: x / e -> x
7: x . (x  y) -> y
8: (y / x) . x -> y
9: x  (x . y) -> y
10: (y . x) / x -> y
11: x / (y  x) -> y
12: (x / y)  x -> y

There are no dependency pairs.
Hence the TRS is trivially terminating.