Given TRS let's call it top-reducible or left-reducible if no rule's right hand side is contained in any rule's left hand side non-trivially.
A term A is contained in an other one B trivially if they overlap at their roots e.g.
2(y) is contained in
1(2(x)) non-trivially while
1(y) is contained in
1(2(x)) trivially) (I also don't know if this 'containment' has a name)
- A TRS with a single rule
1(2(x)) -> 2(x)is not top-reducible.
- A TRS with rules
1(2(x)) -> 3(x),
4(3(5(x,y))) -> 1(5(x,y))is not top-reducible.