YES(?,O(n^1)) 895.06/297.09 YES(?,O(n^1)) 895.06/297.09 895.06/297.09 We are left with following problem, upon which TcT provides the 895.06/297.09 certificate YES(?,O(n^1)). 895.06/297.09 895.06/297.09 Strict Trs: 895.06/297.09 { active(f(X)) -> f(active(X)) 895.06/297.09 , active(f(f(a()))) -> mark(c(f(g(f(a()))))) 895.06/297.09 , active(g(X)) -> g(active(X)) 895.06/297.09 , f(mark(X)) -> mark(f(X)) 895.06/297.09 , f(ok(X)) -> ok(f(X)) 895.06/297.09 , c(ok(X)) -> ok(c(X)) 895.06/297.09 , g(mark(X)) -> mark(g(X)) 895.06/297.09 , g(ok(X)) -> ok(g(X)) 895.06/297.09 , proper(f(X)) -> f(proper(X)) 895.06/297.09 , proper(a()) -> ok(a()) 895.06/297.09 , proper(c(X)) -> c(proper(X)) 895.06/297.09 , proper(g(X)) -> g(proper(X)) 895.06/297.09 , top(mark(X)) -> top(proper(X)) 895.06/297.09 , top(ok(X)) -> top(active(X)) } 895.06/297.09 Obligation: 895.06/297.09 runtime complexity 895.06/297.09 Answer: 895.06/297.09 YES(?,O(n^1)) 895.06/297.09 895.06/297.09 The problem is match-bounded by 2. The enriched problem is 895.06/297.09 compatible with the following automaton. 895.06/297.09 { active_0(3) -> 1 895.06/297.09 , active_0(4) -> 1 895.06/297.09 , active_0(8) -> 1 895.06/297.09 , active_1(3) -> 14 895.06/297.09 , active_1(4) -> 14 895.06/297.09 , active_1(8) -> 14 895.06/297.09 , active_2(13) -> 15 895.06/297.09 , f_0(3) -> 2 895.06/297.09 , f_0(4) -> 2 895.06/297.09 , f_0(8) -> 2 895.06/297.09 , f_1(3) -> 10 895.06/297.09 , f_1(4) -> 10 895.06/297.09 , f_1(8) -> 10 895.06/297.09 , a_0() -> 3 895.06/297.09 , a_1() -> 13 895.06/297.09 , mark_0(3) -> 4 895.06/297.09 , mark_0(4) -> 4 895.06/297.09 , mark_0(8) -> 4 895.06/297.09 , mark_1(10) -> 2 895.06/297.09 , mark_1(10) -> 10 895.06/297.09 , mark_1(12) -> 6 895.06/297.09 , mark_1(12) -> 12 895.06/297.09 , c_0(3) -> 5 895.06/297.09 , c_0(4) -> 5 895.06/297.09 , c_0(8) -> 5 895.06/297.09 , c_1(3) -> 11 895.06/297.09 , c_1(4) -> 11 895.06/297.09 , c_1(8) -> 11 895.06/297.09 , g_0(3) -> 6 895.06/297.09 , g_0(4) -> 6 895.06/297.09 , g_0(8) -> 6 895.06/297.09 , g_1(3) -> 12 895.06/297.09 , g_1(4) -> 12 895.06/297.09 , g_1(8) -> 12 895.06/297.09 , proper_0(3) -> 7 895.06/297.09 , proper_0(4) -> 7 895.06/297.09 , proper_0(8) -> 7 895.06/297.09 , proper_1(3) -> 14 895.06/297.09 , proper_1(4) -> 14 895.06/297.09 , proper_1(8) -> 14 895.06/297.09 , ok_0(3) -> 8 895.06/297.09 , ok_0(4) -> 8 895.06/297.09 , ok_0(8) -> 8 895.06/297.09 , ok_1(10) -> 2 895.06/297.09 , ok_1(10) -> 10 895.06/297.09 , ok_1(11) -> 5 895.06/297.09 , ok_1(11) -> 11 895.06/297.09 , ok_1(12) -> 6 895.06/297.09 , ok_1(12) -> 12 895.06/297.09 , ok_1(13) -> 7 895.06/297.09 , ok_1(13) -> 14 895.06/297.09 , top_0(3) -> 9 895.06/297.09 , top_0(4) -> 9 895.06/297.09 , top_0(8) -> 9 895.06/297.09 , top_1(14) -> 9 895.06/297.09 , top_2(15) -> 9 } 895.06/297.09 895.06/297.09 Hurray, we answered YES(?,O(n^1)) 895.43/297.16 EOF