We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { rev_l#2(x8, x10) -> Cons(x10, x8) , step_x_f#1(rev_l(), x5, step_x_f(x2, x3, x4), x1) -> step_x_f#1(x2, x3, x4, rev_l#2(x1, x5)) , step_x_f#1(rev_l(), x5, fleft_op_e_xs_1(), x3) -> rev_l#2(x3, x5) , foldr#3(Cons(x16, x6)) -> step_x_f(rev_l(), x16, foldr#3(x6)) , foldr#3(Nil()) -> fleft_op_e_xs_1() , main(Cons(x8, x9)) -> step_x_f#1(rev_l(), x8, foldr#3(x9), Nil()) , main(Nil()) -> Nil() } Obligation: innermost runtime complexity Answer: YES(?,O(n^1)) The problem is match-bounded by 3. The enriched problem is compatible with the following automaton. { rev_l#2_0(2, 2) -> 1 , rev_l#2_1(1, 2) -> 1 , rev_l#2_1(2, 2) -> 1 , rev_l#2_1(2, 2) -> 3 , rev_l#2_1(3, 2) -> 1 , rev_l#2_2(1, 2) -> 1 , rev_l#2_2(6, 2) -> 1 , Cons_0(2, 2) -> 2 , Cons_1(2, 2) -> 1 , Cons_2(2, 1) -> 1 , Cons_2(2, 2) -> 1 , Cons_2(2, 2) -> 3 , Cons_2(2, 3) -> 1 , Cons_3(2, 1) -> 1 , Cons_3(2, 6) -> 1 , step_x_f#1_0(2, 2, 2, 2) -> 1 , step_x_f#1_1(2, 2, 2, 1) -> 1 , step_x_f#1_1(2, 2, 2, 3) -> 1 , step_x_f#1_1(4, 2, 5, 6) -> 1 , step_x_f#1_2(4, 2, 5, 1) -> 1 , rev_l_0() -> 2 , rev_l_1() -> 4 , step_x_f_0(2, 2, 2) -> 2 , step_x_f_1(4, 2, 5) -> 1 , step_x_f_1(4, 2, 5) -> 5 , fleft_op_e_xs_1_0() -> 2 , fleft_op_e_xs_1_1() -> 1 , fleft_op_e_xs_1_1() -> 5 , foldr#3_0(2) -> 1 , foldr#3_1(2) -> 5 , Nil_0() -> 2 , Nil_1() -> 1 , Nil_1() -> 6 , main_0(2) -> 1 } Hurray, we answered YES(?,O(n^1))