YES(?,O(n^1)) 0.00/0.99 YES(?,O(n^1)) 0.00/0.99 0.00/0.99 We are left with following problem, upon which TcT provides the 0.00/0.99 certificate YES(?,O(n^1)). 0.00/0.99 0.00/0.99 Strict Trs: 0.00/0.99 { concat(leaf(), Y) -> Y 0.00/0.99 , concat(cons(U, V), Y) -> cons(U, concat(V, Y)) 0.00/0.99 , lessleaves(X, leaf()) -> false() 0.00/0.99 , lessleaves(leaf(), cons(W, Z)) -> true() 0.00/0.99 , lessleaves(cons(U, V), cons(W, Z)) -> 0.00/0.99 lessleaves(concat(U, V), concat(W, Z)) } 0.00/0.99 Obligation: 0.00/0.99 innermost runtime complexity 0.00/0.99 Answer: 0.00/0.99 YES(?,O(n^1)) 0.00/0.99 0.00/0.99 The problem is match-bounded by 2. The enriched problem is 0.00/0.99 compatible with the following automaton. 0.00/0.99 { concat_0(2, 2) -> 1 0.00/0.99 , concat_1(2, 2) -> 3 0.00/0.99 , concat_1(2, 2) -> 4 0.00/0.99 , concat_1(2, 2) -> 5 0.00/0.99 , concat_1(2, 3) -> 3 0.00/0.99 , concat_1(2, 3) -> 4 0.00/0.99 , concat_1(2, 3) -> 5 0.00/0.99 , concat_2(2, 3) -> 4 0.00/0.99 , concat_2(2, 3) -> 5 0.00/0.99 , leaf_0() -> 1 0.00/0.99 , leaf_0() -> 2 0.00/0.99 , leaf_0() -> 3 0.00/0.99 , leaf_0() -> 4 0.00/0.99 , leaf_0() -> 5 0.00/0.99 , cons_0(2, 2) -> 1 0.00/0.99 , cons_0(2, 2) -> 2 0.00/0.99 , cons_0(2, 2) -> 3 0.00/0.99 , cons_0(2, 2) -> 4 0.00/0.99 , cons_0(2, 2) -> 5 0.00/0.99 , cons_1(2, 3) -> 1 0.00/0.99 , cons_1(2, 3) -> 3 0.00/0.99 , cons_1(2, 3) -> 4 0.00/0.99 , cons_1(2, 3) -> 5 0.00/0.99 , lessleaves_0(2, 2) -> 1 0.00/0.99 , lessleaves_1(3, 3) -> 1 0.00/0.99 , lessleaves_2(4, 5) -> 1 0.00/0.99 , false_0() -> 1 0.00/0.99 , false_0() -> 2 0.00/0.99 , false_0() -> 3 0.00/0.99 , false_0() -> 4 0.00/0.99 , false_0() -> 5 0.00/0.99 , false_1() -> 1 0.00/0.99 , true_0() -> 1 0.00/0.99 , true_0() -> 2 0.00/0.99 , true_0() -> 3 0.00/0.99 , true_0() -> 4 0.00/0.99 , true_0() -> 5 0.00/0.99 , true_1() -> 1 } 0.00/0.99 0.00/0.99 Hurray, we answered YES(?,O(n^1)) 0.00/1.00 EOF