YES(?,O(n^1))
4.00/1.51	YES(?,O(n^1))
4.00/1.51	
4.00/1.51	We are left with following problem, upon which TcT provides the
4.00/1.51	certificate YES(?,O(n^1)).
4.00/1.51	
4.00/1.51	Strict Trs:
4.00/1.51	  { active(c()) -> mark(f(g(c())))
4.00/1.51	  , active(f(g(X))) -> mark(g(X))
4.00/1.51	  , mark(c()) -> active(c())
4.00/1.51	  , mark(f(X)) -> active(f(X))
4.00/1.51	  , mark(g(X)) -> active(g(X))
4.00/1.51	  , f(active(X)) -> f(X)
4.00/1.51	  , f(mark(X)) -> f(X)
4.00/1.51	  , g(active(X)) -> g(X)
4.00/1.51	  , g(mark(X)) -> g(X) }
4.00/1.51	Obligation:
4.00/1.51	  derivational complexity
4.00/1.51	Answer:
4.00/1.51	  YES(?,O(n^1))
4.00/1.51	
4.00/1.51	The problem is match-bounded by 4. The enriched problem is
4.00/1.51	compatible with the following automaton.
4.00/1.51	{ active_0(1) -> 1
4.00/1.51	, active_0(2) -> 1
4.00/1.51	, active_0(3) -> 1
4.00/1.51	, active_0(4) -> 1
4.00/1.51	, active_0(5) -> 1
4.00/1.51	, active_1(4) -> 3
4.00/1.51	, active_1(5) -> 3
4.00/1.51	, active_1(6) -> 3
4.00/1.51	, active_1(8) -> 3
4.00/1.51	, active_1(9) -> 1
4.00/1.51	, active_2(6) -> 1
4.00/1.51	, active_2(6) -> 3
4.00/1.51	, active_2(9) -> 1
4.00/1.51	, active_2(9) -> 3
4.00/1.51	, active_2(11) -> 1
4.00/1.51	, active_2(11) -> 3
4.00/1.51	, active_3(9) -> 1
4.00/1.51	, active_3(9) -> 3
4.00/1.51	, active_3(13) -> 1
4.00/1.51	, active_3(13) -> 3
4.00/1.51	, active_3(14) -> 3
4.00/1.51	, active_4(15) -> 1
4.00/1.51	, active_4(15) -> 3
4.00/1.51	, c_0() -> 2
4.00/1.51	, c_1() -> 8
4.00/1.51	, c_2() -> 12
4.00/1.51	, mark_0(1) -> 3
4.00/1.51	, mark_0(2) -> 3
4.00/1.51	, mark_0(3) -> 3
4.00/1.51	, mark_0(4) -> 3
4.00/1.51	, mark_0(5) -> 3
4.00/1.51	, mark_1(5) -> 1
4.00/1.51	, mark_1(5) -> 3
4.00/1.51	, mark_1(6) -> 1
4.00/1.51	, mark_1(9) -> 3
4.00/1.51	, mark_2(6) -> 3
4.00/1.51	, mark_2(9) -> 1
4.00/1.51	, mark_2(9) -> 3
4.00/1.51	, mark_2(10) -> 3
4.00/1.51	, mark_2(11) -> 3
4.00/1.51	, mark_3(14) -> 1
4.00/1.51	, mark_3(14) -> 3
4.00/1.51	, f_0(1) -> 4
4.00/1.51	, f_0(2) -> 4
4.00/1.51	, f_0(3) -> 4
4.00/1.51	, f_0(4) -> 4
4.00/1.51	, f_0(5) -> 4
4.00/1.51	, f_1(1) -> 4
4.00/1.51	, f_1(1) -> 8
4.00/1.51	, f_1(2) -> 4
4.00/1.51	, f_1(2) -> 8
4.00/1.51	, f_1(3) -> 4
4.00/1.51	, f_1(3) -> 8
4.00/1.51	, f_1(4) -> 4
4.00/1.51	, f_1(4) -> 8
4.00/1.51	, f_1(5) -> 4
4.00/1.51	, f_1(5) -> 8
4.00/1.51	, f_1(6) -> 4
4.00/1.51	, f_1(7) -> 6
4.00/1.51	, f_1(8) -> 4
4.00/1.51	, f_1(9) -> 4
4.00/1.51	, f_1(10) -> 4
4.00/1.51	, f_1(11) -> 4
4.00/1.51	, f_1(13) -> 4
4.00/1.51	, f_1(14) -> 4
4.00/1.51	, f_1(15) -> 4
4.00/1.51	, f_2(4) -> 4
4.00/1.51	, f_2(4) -> 8
4.00/1.51	, f_2(5) -> 4
4.00/1.51	, f_2(5) -> 8
4.00/1.51	, f_2(6) -> 4
4.00/1.51	, f_2(6) -> 8
4.00/1.51	, f_2(7) -> 9
4.00/1.51	, f_2(8) -> 4
4.00/1.51	, f_2(8) -> 8
4.00/1.51	, f_2(9) -> 4
4.00/1.51	, f_2(9) -> 8
4.00/1.51	, f_2(10) -> 4
4.00/1.51	, f_2(10) -> 8
4.00/1.51	, f_2(11) -> 4
4.00/1.51	, f_2(11) -> 8
4.00/1.51	, f_2(11) -> 10
4.00/1.51	, f_2(13) -> 4
4.00/1.51	, f_2(13) -> 8
4.00/1.51	, f_2(14) -> 4
4.00/1.51	, f_2(14) -> 8
4.00/1.51	, f_2(15) -> 4
4.00/1.51	, f_2(15) -> 8
4.00/1.51	, f_3(7) -> 13
4.00/1.51	, f_3(11) -> 13
4.00/1.51	, g_0(1) -> 5
4.00/1.51	, g_0(2) -> 5
4.00/1.51	, g_0(3) -> 5
4.00/1.51	, g_0(4) -> 5
4.00/1.51	, g_0(5) -> 5
4.00/1.51	, g_1(1) -> 5
4.00/1.51	, g_1(1) -> 6
4.00/1.51	, g_1(1) -> 9
4.00/1.51	, g_1(1) -> 13
4.00/1.51	, g_1(2) -> 5
4.00/1.51	, g_1(2) -> 6
4.00/1.51	, g_1(2) -> 9
4.00/1.51	, g_1(2) -> 13
4.00/1.51	, g_1(3) -> 5
4.00/1.51	, g_1(3) -> 6
4.00/1.51	, g_1(3) -> 9
4.00/1.51	, g_1(3) -> 13
4.00/1.51	, g_1(4) -> 5
4.00/1.51	, g_1(4) -> 6
4.00/1.51	, g_1(4) -> 9
4.00/1.51	, g_1(4) -> 13
4.00/1.51	, g_1(5) -> 5
4.00/1.51	, g_1(5) -> 6
4.00/1.51	, g_1(5) -> 9
4.00/1.51	, g_1(5) -> 13
4.00/1.51	, g_1(6) -> 5
4.00/1.51	, g_1(8) -> 5
4.00/1.51	, g_1(8) -> 7
4.00/1.51	, g_1(9) -> 5
4.00/1.51	, g_1(10) -> 5
4.00/1.51	, g_1(11) -> 5
4.00/1.51	, g_1(12) -> 5
4.00/1.51	, g_1(13) -> 5
4.00/1.51	, g_1(14) -> 5
4.00/1.51	, g_1(15) -> 5
4.00/1.51	, g_2(1) -> 9
4.00/1.51	, g_2(2) -> 9
4.00/1.51	, g_2(3) -> 9
4.00/1.51	, g_2(4) -> 5
4.00/1.51	, g_2(4) -> 6
4.00/1.51	, g_2(4) -> 9
4.00/1.51	, g_2(4) -> 13
4.00/1.51	, g_2(5) -> 5
4.00/1.51	, g_2(5) -> 6
4.00/1.51	, g_2(5) -> 9
4.00/1.51	, g_2(5) -> 13
4.00/1.51	, g_2(6) -> 5
4.00/1.51	, g_2(6) -> 6
4.00/1.51	, g_2(6) -> 9
4.00/1.51	, g_2(6) -> 13
4.00/1.51	, g_2(8) -> 5
4.00/1.51	, g_2(8) -> 6
4.00/1.51	, g_2(8) -> 9
4.00/1.51	, g_2(8) -> 13
4.00/1.51	, g_2(9) -> 5
4.00/1.51	, g_2(9) -> 6
4.00/1.51	, g_2(9) -> 9
4.00/1.51	, g_2(9) -> 13
4.00/1.51	, g_2(10) -> 5
4.00/1.51	, g_2(10) -> 6
4.00/1.51	, g_2(10) -> 9
4.00/1.51	, g_2(10) -> 13
4.00/1.51	, g_2(11) -> 5
4.00/1.51	, g_2(11) -> 6
4.00/1.51	, g_2(11) -> 9
4.00/1.51	, g_2(11) -> 13
4.00/1.51	, g_2(12) -> 11
4.00/1.51	, g_2(13) -> 5
4.00/1.51	, g_2(13) -> 6
4.00/1.51	, g_2(13) -> 9
4.00/1.51	, g_2(13) -> 13
4.00/1.51	, g_2(14) -> 5
4.00/1.51	, g_2(14) -> 6
4.00/1.51	, g_2(14) -> 9
4.00/1.51	, g_2(14) -> 13
4.00/1.51	, g_2(15) -> 5
4.00/1.51	, g_2(15) -> 6
4.00/1.51	, g_2(15) -> 9
4.00/1.51	, g_2(15) -> 13
4.00/1.51	, g_3(1) -> 13
4.00/1.51	, g_3(2) -> 13
4.00/1.51	, g_3(3) -> 13
4.00/1.51	, g_3(4) -> 13
4.00/1.51	, g_3(5) -> 13
4.00/1.51	, g_3(6) -> 9
4.00/1.51	, g_3(6) -> 13
4.00/1.51	, g_3(8) -> 13
4.00/1.51	, g_3(9) -> 9
4.00/1.51	, g_3(9) -> 13
4.00/1.51	, g_3(10) -> 9
4.00/1.51	, g_3(10) -> 13
4.00/1.51	, g_3(11) -> 9
4.00/1.51	, g_3(11) -> 13
4.00/1.51	, g_3(12) -> 14
4.00/1.51	, g_3(13) -> 9
4.00/1.51	, g_3(14) -> 9
4.00/1.51	, g_3(15) -> 9
4.00/1.51	, g_4(9) -> 13
4.00/1.51	, g_4(12) -> 15
4.00/1.51	, g_4(13) -> 13
4.00/1.51	, g_4(14) -> 13
4.00/1.51	, g_4(15) -> 13 }
4.00/1.51	
4.00/1.51	Hurray, we answered YES(?,O(n^1))
4.00/1.52	EOF