YES(?,O(n^1)) We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { rec[revApp_0][2](Nil(), Cons(x1, x2)) -> Cons(x1, x2) , rec[revApp_0][2](Cons(x14, x10), x6) -> rec[revApp_0][2](x10, Cons(x14, x6)) , rec[dfsAcc_0][3](Leaf(x40), x56) -> Cons(x40, x56) , rec[dfsAcc_0][3](Node(x14, x10), x6) -> rec[dfsAcc_0][3](x10, rec[dfsAcc_0][3](x14, x6)) , main(x1) -> rec[revApp_0][2](rec[dfsAcc_0][3](x1, Nil()), Nil()) } Obligation: innermost runtime complexity Answer: YES(?,O(n^1)) The problem is match-bounded by 2. The enriched problem is compatible with the following automaton. { Nil_0() -> 2 , Nil_1() -> 1 , Nil_1() -> 4 , Cons_0(2, 2) -> 2 , Cons_1(2, 1) -> 1 , Cons_1(2, 2) -> 1 , Cons_1(2, 2) -> 2 , Cons_1(2, 2) -> 3 , Cons_1(2, 3) -> 1 , Cons_1(2, 3) -> 3 , Cons_1(2, 4) -> 1 , Cons_1(2, 4) -> 2 , Cons_1(2, 5) -> 1 , Cons_2(2, 1) -> 1 , Cons_2(2, 1) -> 5 , Cons_2(2, 2) -> 1 , Cons_2(2, 3) -> 1 , Cons_2(2, 5) -> 1 , Cons_2(2, 5) -> 5 , rec[revApp_0][2]_0(2, 2) -> 1 , rec[revApp_0][2]_1(2, 1) -> 1 , rec[revApp_0][2]_1(4, 3) -> 1 , rec[revApp_0][2]_2(2, 5) -> 1 , rec[revApp_0][2]_2(4, 5) -> 1 , Leaf_0(2) -> 2 , rec[dfsAcc_0][3]_0(2, 2) -> 1 , rec[dfsAcc_0][3]_1(2, 2) -> 2 , rec[dfsAcc_0][3]_1(2, 2) -> 3 , rec[dfsAcc_0][3]_1(2, 3) -> 1 , rec[dfsAcc_0][3]_1(2, 3) -> 3 , rec[dfsAcc_0][3]_1(2, 4) -> 2 , Node_0(2, 2) -> 2 , main_0(2) -> 1 } Hurray, we answered YES(?,O(n^1))