YES(?,O(n^1))
814.20/241.26	YES(?,O(n^1))
814.20/241.26	
814.20/241.26	We are left with following problem, upon which TcT provides the
814.20/241.26	certificate YES(?,O(n^1)).
814.20/241.26	
814.20/241.26	Strict Trs:
814.20/241.26	  { active(f(X)) -> f(active(X))
814.20/241.26	  , active(f(f(a()))) -> mark(c(f(g(f(a())))))
814.20/241.26	  , active(g(X)) -> g(active(X))
814.20/241.26	  , f(mark(X)) -> mark(f(X))
814.20/241.26	  , f(ok(X)) -> ok(f(X))
814.20/241.26	  , c(ok(X)) -> ok(c(X))
814.20/241.26	  , g(mark(X)) -> mark(g(X))
814.20/241.26	  , g(ok(X)) -> ok(g(X))
814.20/241.26	  , proper(f(X)) -> f(proper(X))
814.20/241.26	  , proper(a()) -> ok(a())
814.20/241.26	  , proper(c(X)) -> c(proper(X))
814.20/241.26	  , proper(g(X)) -> g(proper(X))
814.20/241.26	  , top(mark(X)) -> top(proper(X))
814.20/241.26	  , top(ok(X)) -> top(active(X)) }
814.20/241.26	Obligation:
814.20/241.26	  innermost runtime complexity
814.20/241.26	Answer:
814.20/241.26	  YES(?,O(n^1))
814.20/241.26	
814.20/241.26	The problem is match-bounded by 2. The enriched problem is
814.20/241.26	compatible with the following automaton.
814.20/241.26	{ active_0(3) -> 1
814.20/241.26	, active_0(4) -> 1
814.20/241.26	, active_0(8) -> 1
814.20/241.26	, active_1(3) -> 14
814.20/241.26	, active_1(4) -> 14
814.20/241.26	, active_1(8) -> 14
814.20/241.26	, active_2(13) -> 15
814.20/241.26	, f_0(3) -> 2
814.20/241.26	, f_0(4) -> 2
814.20/241.26	, f_0(8) -> 2
814.20/241.26	, f_1(3) -> 10
814.20/241.26	, f_1(4) -> 10
814.20/241.26	, f_1(8) -> 10
814.20/241.26	, a_0() -> 3
814.20/241.26	, a_1() -> 13
814.20/241.26	, mark_0(3) -> 4
814.20/241.26	, mark_0(4) -> 4
814.20/241.26	, mark_0(8) -> 4
814.20/241.26	, mark_1(10) -> 2
814.20/241.26	, mark_1(10) -> 10
814.20/241.26	, mark_1(12) -> 6
814.20/241.26	, mark_1(12) -> 12
814.20/241.26	, c_0(3) -> 5
814.20/241.26	, c_0(4) -> 5
814.20/241.26	, c_0(8) -> 5
814.20/241.26	, c_1(3) -> 11
814.20/241.26	, c_1(4) -> 11
814.20/241.26	, c_1(8) -> 11
814.20/241.26	, g_0(3) -> 6
814.20/241.26	, g_0(4) -> 6
814.20/241.26	, g_0(8) -> 6
814.20/241.26	, g_1(3) -> 12
814.20/241.26	, g_1(4) -> 12
814.20/241.26	, g_1(8) -> 12
814.20/241.26	, proper_0(3) -> 7
814.20/241.26	, proper_0(4) -> 7
814.20/241.26	, proper_0(8) -> 7
814.20/241.26	, proper_1(3) -> 14
814.20/241.26	, proper_1(4) -> 14
814.20/241.26	, proper_1(8) -> 14
814.20/241.26	, ok_0(3) -> 8
814.20/241.26	, ok_0(4) -> 8
814.20/241.26	, ok_0(8) -> 8
814.20/241.26	, ok_1(10) -> 2
814.20/241.26	, ok_1(10) -> 10
814.20/241.26	, ok_1(11) -> 5
814.20/241.26	, ok_1(11) -> 11
814.20/241.26	, ok_1(12) -> 6
814.20/241.26	, ok_1(12) -> 12
814.20/241.26	, ok_1(13) -> 7
814.20/241.26	, ok_1(13) -> 14
814.20/241.26	, top_0(3) -> 9
814.20/241.26	, top_0(4) -> 9
814.20/241.26	, top_0(8) -> 9
814.20/241.26	, top_1(14) -> 9
814.20/241.26	, top_2(15) -> 9 }
814.20/241.26	
814.20/241.26	Hurray, we answered YES(?,O(n^1))
814.20/241.26	EOF