We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { rev(a()) -> a() , rev(b()) -> b() , rev(++(x, x)) -> rev(x) , rev(++(x, y)) -> ++(rev(y), rev(x)) } 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_1(2) -> 1 , a_0() -> 2 , a_1() -> 1 , b_0() -> 2 , b_1() -> 1 , ++_0(2, 2) -> 2 , ++_1(1, 1) -> 1 } Hurray, we answered YES(?,O(n^1))