YES(?,O(n^1)) 840.00/297.07 YES(?,O(n^1)) 840.00/297.07 840.00/297.07 We are left with following problem, upon which TcT provides the 840.00/297.07 certificate YES(?,O(n^1)). 840.00/297.07 840.00/297.07 Strict Trs: 840.00/297.07 { active(f(X)) -> f(active(X)) 840.00/297.07 , active(f(0())) -> mark(cons(0(), f(s(0())))) 840.00/297.07 , active(f(s(0()))) -> mark(f(p(s(0())))) 840.00/297.07 , active(cons(X1, X2)) -> cons(active(X1), X2) 840.00/297.07 , active(s(X)) -> s(active(X)) 840.00/297.07 , active(p(X)) -> p(active(X)) 840.00/297.07 , active(p(s(0()))) -> mark(0()) 840.00/297.07 , f(mark(X)) -> mark(f(X)) 840.00/297.07 , f(ok(X)) -> ok(f(X)) 840.00/297.07 , cons(mark(X1), X2) -> mark(cons(X1, X2)) 840.00/297.07 , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 840.00/297.07 , s(mark(X)) -> mark(s(X)) 840.00/297.07 , s(ok(X)) -> ok(s(X)) 840.00/297.07 , p(mark(X)) -> mark(p(X)) 840.00/297.07 , p(ok(X)) -> ok(p(X)) 840.00/297.07 , proper(f(X)) -> f(proper(X)) 840.00/297.07 , proper(0()) -> ok(0()) 840.00/297.07 , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 840.00/297.07 , proper(s(X)) -> s(proper(X)) 840.00/297.07 , proper(p(X)) -> p(proper(X)) 840.00/297.07 , top(mark(X)) -> top(proper(X)) 840.00/297.07 , top(ok(X)) -> top(active(X)) } 840.00/297.07 Obligation: 840.00/297.07 runtime complexity 840.00/297.07 Answer: 840.00/297.07 YES(?,O(n^1)) 840.00/297.07 840.00/297.07 The problem is match-bounded by 2. The enriched problem is 840.00/297.07 compatible with the following automaton. 840.00/297.07 { active_0(3) -> 1 840.00/297.07 , active_0(4) -> 1 840.00/297.07 , active_0(9) -> 1 840.00/297.07 , active_1(3) -> 16 840.00/297.07 , active_1(4) -> 16 840.00/297.07 , active_1(9) -> 16 840.00/297.07 , active_2(15) -> 17 840.00/297.07 , f_0(3) -> 2 840.00/297.07 , f_0(4) -> 2 840.00/297.07 , f_0(9) -> 2 840.00/297.07 , f_1(3) -> 11 840.00/297.07 , f_1(4) -> 11 840.00/297.07 , f_1(9) -> 11 840.00/297.07 , 0_0() -> 3 840.00/297.07 , 0_1() -> 15 840.00/297.07 , mark_0(3) -> 4 840.00/297.07 , mark_0(4) -> 4 840.00/297.07 , mark_0(9) -> 4 840.00/297.07 , mark_1(11) -> 2 840.00/297.07 , mark_1(11) -> 11 840.00/297.07 , mark_1(12) -> 5 840.00/297.07 , mark_1(12) -> 12 840.00/297.07 , mark_1(13) -> 6 840.00/297.07 , mark_1(13) -> 13 840.00/297.07 , mark_1(14) -> 7 840.00/297.07 , mark_1(14) -> 14 840.00/297.07 , cons_0(3, 3) -> 5 840.00/297.07 , cons_0(3, 4) -> 5 840.00/297.07 , cons_0(3, 9) -> 5 840.00/297.07 , cons_0(4, 3) -> 5 840.00/297.07 , cons_0(4, 4) -> 5 840.00/297.07 , cons_0(4, 9) -> 5 840.00/297.07 , cons_0(9, 3) -> 5 840.00/297.07 , cons_0(9, 4) -> 5 840.00/297.07 , cons_0(9, 9) -> 5 840.00/297.07 , cons_1(3, 3) -> 12 840.00/297.07 , cons_1(3, 4) -> 12 840.00/297.07 , cons_1(3, 9) -> 12 840.00/297.07 , cons_1(4, 3) -> 12 840.00/297.07 , cons_1(4, 4) -> 12 840.00/297.07 , cons_1(4, 9) -> 12 840.00/297.07 , cons_1(9, 3) -> 12 840.00/297.07 , cons_1(9, 4) -> 12 840.00/297.07 , cons_1(9, 9) -> 12 840.00/297.07 , s_0(3) -> 6 840.00/297.07 , s_0(4) -> 6 840.00/297.07 , s_0(9) -> 6 840.00/297.07 , s_1(3) -> 13 840.00/297.07 , s_1(4) -> 13 840.00/297.07 , s_1(9) -> 13 840.00/297.07 , p_0(3) -> 7 840.00/297.07 , p_0(4) -> 7 840.00/297.07 , p_0(9) -> 7 840.00/297.07 , p_1(3) -> 14 840.00/297.07 , p_1(4) -> 14 840.00/297.07 , p_1(9) -> 14 840.00/297.07 , proper_0(3) -> 8 840.00/297.07 , proper_0(4) -> 8 840.00/297.07 , proper_0(9) -> 8 840.00/297.07 , proper_1(3) -> 16 840.00/297.07 , proper_1(4) -> 16 840.00/297.07 , proper_1(9) -> 16 840.00/297.07 , ok_0(3) -> 9 840.00/297.07 , ok_0(4) -> 9 840.00/297.07 , ok_0(9) -> 9 840.00/297.07 , ok_1(11) -> 2 840.00/297.07 , ok_1(11) -> 11 840.00/297.07 , ok_1(12) -> 5 840.00/297.07 , ok_1(12) -> 12 840.00/297.07 , ok_1(13) -> 6 840.00/297.07 , ok_1(13) -> 13 840.00/297.07 , ok_1(14) -> 7 840.00/297.07 , ok_1(14) -> 14 840.00/297.07 , ok_1(15) -> 8 840.00/297.07 , ok_1(15) -> 16 840.00/297.07 , top_0(3) -> 10 840.00/297.07 , top_0(4) -> 10 840.00/297.07 , top_0(9) -> 10 840.00/297.07 , top_1(16) -> 10 840.00/297.07 , top_2(17) -> 10 } 840.00/297.07 840.00/297.07 Hurray, we answered YES(?,O(n^1)) 840.00/297.08 EOF