YES(?,O(n^1)) 153.78/39.44 YES(?,O(n^1)) 153.78/39.44 153.78/39.44 We are left with following problem, upon which TcT provides the 153.78/39.44 certificate YES(?,O(n^1)). 153.78/39.44 153.78/39.44 Strict Trs: 153.78/39.44 { active(f(X)) -> f(active(X)) 153.78/39.44 , active(f(X)) -> mark(g(h(f(X)))) 153.78/39.44 , active(h(X)) -> h(active(X)) 153.78/39.44 , f(mark(X)) -> mark(f(X)) 153.78/39.44 , f(ok(X)) -> ok(f(X)) 153.78/39.44 , g(ok(X)) -> ok(g(X)) 153.78/39.44 , h(mark(X)) -> mark(h(X)) 153.78/39.44 , h(ok(X)) -> ok(h(X)) 153.78/39.44 , proper(f(X)) -> f(proper(X)) 153.78/39.44 , proper(g(X)) -> g(proper(X)) 153.78/39.44 , proper(h(X)) -> h(proper(X)) 153.78/39.44 , top(mark(X)) -> top(proper(X)) 153.78/39.44 , top(ok(X)) -> top(active(X)) } 153.78/39.44 Obligation: 153.78/39.44 runtime complexity 153.78/39.44 Answer: 153.78/39.44 YES(?,O(n^1)) 153.78/39.44 153.78/39.44 The problem is match-bounded by 1. The enriched problem is 153.78/39.44 compatible with the following automaton. 153.78/39.44 { active_0(2) -> 1 153.78/39.44 , active_1(2) -> 4 153.78/39.44 , f_0(2) -> 1 153.78/39.44 , f_1(2) -> 3 153.78/39.44 , mark_0(2) -> 2 153.78/39.44 , mark_1(3) -> 1 153.78/39.44 , mark_1(3) -> 3 153.78/39.44 , g_0(2) -> 1 153.78/39.44 , g_1(2) -> 3 153.78/39.44 , h_0(2) -> 1 153.78/39.44 , h_1(2) -> 3 153.78/39.44 , proper_0(2) -> 1 153.78/39.44 , proper_1(2) -> 4 153.78/39.44 , ok_0(2) -> 2 153.78/39.44 , ok_1(3) -> 1 153.78/39.44 , ok_1(3) -> 3 153.78/39.44 , top_0(2) -> 1 153.78/39.44 , top_1(4) -> 1 } 153.78/39.44 153.78/39.44 Hurray, we answered YES(?,O(n^1)) 153.78/39.47 EOF