YES(?,O(n^1)) 0.00/0.63 YES(?,O(n^1)) 0.00/0.63 0.00/0.63 We are left with following problem, upon which TcT provides the 0.00/0.63 certificate YES(?,O(n^1)). 0.00/0.63 0.00/0.63 Strict Trs: 0.00/0.63 { @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) 0.00/0.63 , @(Nil(), ys) -> ys 0.00/0.63 , game(p1, p2, Cons(Capture(), xs)) -> 0.00/0.63 game[Ite][False][Ite][False][Ite](True(), 0.00/0.63 p1, 0.00/0.63 p2, 0.00/0.63 Cons(Capture(), xs)) 0.00/0.63 , game(p1, p2, Cons(Swap(), xs)) -> game(p2, p1, xs) 0.00/0.63 , game(p1, p2, Nil()) -> @(p1, p2) 0.00/0.63 , equal(Capture(), Capture()) -> True() 0.00/0.63 , equal(Capture(), Swap()) -> False() 0.00/0.63 , equal(Swap(), Capture()) -> False() 0.00/0.63 , equal(Swap(), Swap()) -> True() 0.00/0.63 , goal(p1, p2, moves) -> game(p1, p2, moves) } 0.00/0.63 Obligation: 0.00/0.63 innermost runtime complexity 0.00/0.63 Answer: 0.00/0.63 YES(?,O(n^1)) 0.00/0.63 0.00/0.63 The problem is match-bounded by 1. The enriched problem is 0.00/0.63 compatible with the following automaton. 0.00/0.63 { @_0(2, 2) -> 1 0.00/0.63 , @_1(2, 2) -> 1 0.00/0.63 , @_1(2, 2) -> 3 0.00/0.63 , Cons_0(2, 2) -> 1 0.00/0.63 , Cons_0(2, 2) -> 2 0.00/0.63 , Cons_0(2, 2) -> 3 0.00/0.63 , Cons_1(2, 3) -> 1 0.00/0.63 , Cons_1(2, 3) -> 3 0.00/0.63 , Cons_1(6, 2) -> 5 0.00/0.63 , Nil_0() -> 1 0.00/0.63 , Nil_0() -> 2 0.00/0.63 , Nil_0() -> 3 0.00/0.63 , game_0(2, 2, 2) -> 1 0.00/0.63 , game_1(2, 2, 2) -> 1 0.00/0.63 , Capture_0() -> 1 0.00/0.63 , Capture_0() -> 2 0.00/0.63 , Capture_0() -> 3 0.00/0.63 , Capture_1() -> 6 0.00/0.63 , game[Ite][False][Ite][False][Ite]_0(2, 2, 2, 2) -> 1 0.00/0.63 , game[Ite][False][Ite][False][Ite]_0(2, 2, 2, 2) -> 2 0.00/0.63 , game[Ite][False][Ite][False][Ite]_0(2, 2, 2, 2) -> 3 0.00/0.63 , game[Ite][False][Ite][False][Ite]_1(4, 2, 2, 5) -> 1 0.00/0.63 , True_0() -> 1 0.00/0.63 , True_0() -> 2 0.00/0.63 , True_0() -> 3 0.00/0.63 , True_1() -> 1 0.00/0.63 , True_1() -> 4 0.00/0.63 , Swap_0() -> 1 0.00/0.63 , Swap_0() -> 2 0.00/0.63 , Swap_0() -> 3 0.00/0.63 , equal_0(2, 2) -> 1 0.00/0.63 , False_0() -> 1 0.00/0.63 , False_0() -> 2 0.00/0.63 , False_0() -> 3 0.00/0.63 , False_1() -> 1 0.00/0.63 , goal_0(2, 2, 2) -> 1 } 0.00/0.63 0.00/0.63 Hurray, we answered YES(?,O(n^1)) 0.00/0.64 EOF