YES(?,O(n^1)) We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { rev(rev(x)) -> x , rev(nil()) -> nil() , rev(++(x, y)) -> ++(rev(y), rev(x)) , ++(x, nil()) -> x , ++(x, ++(y, z)) -> ++(++(x, y), z) , ++(nil(), y) -> y , ++(.(x, y), z) -> .(x, ++(y, z)) , make(x) -> .(x, nil()) } Obligation: innermost runtime complexity Answer: YES(?,O(n^1)) The problem is match-bounded by 1. The enriched problem is compatible with the following automaton. { rev_0(2) -> 1 , rev_0(4) -> 1 , nil_0() -> 2 , nil_0() -> 3 , nil_0() -> 6 , nil_1() -> 1 , ++_0(2, 2) -> 3 , ++_0(2, 4) -> 3 , ++_0(4, 2) -> 3 , ++_0(4, 4) -> 3 , ++_1(2, 2) -> 6 , ++_1(2, 4) -> 6 , ++_1(4, 2) -> 6 , ++_1(4, 4) -> 6 , ._0(2, 2) -> 3 , ._0(2, 2) -> 4 , ._0(2, 2) -> 6 , ._0(2, 4) -> 3 , ._0(2, 4) -> 4 , ._0(2, 4) -> 6 , ._0(4, 2) -> 3 , ._0(4, 2) -> 4 , ._0(4, 2) -> 6 , ._0(4, 4) -> 3 , ._0(4, 4) -> 4 , ._0(4, 4) -> 6 , ._1(2, 1) -> 5 , ._1(2, 6) -> 3 , ._1(2, 6) -> 6 , ._1(4, 1) -> 5 , ._1(4, 6) -> 3 , ._1(4, 6) -> 6 , make_0(2) -> 5 , make_0(4) -> 5 , 2 -> 3 , 2 -> 6 , 4 -> 3 , 4 -> 6 } Hurray, we answered YES(?,O(n^1))