YES(?,O(n^1))
822.52/297.10	YES(?,O(n^1))
822.52/297.10	
822.52/297.10	We are left with following problem, upon which TcT provides the
822.52/297.10	certificate YES(?,O(n^1)).
822.52/297.10	
822.52/297.10	Strict Trs:
822.52/297.10	  { active(and(X1, X2)) -> and(active(X1), X2)
822.52/297.10	  , active(and(tt(), X)) -> mark(X)
822.52/297.10	  , active(plus(X1, X2)) -> plus(X1, active(X2))
822.52/297.10	  , active(plus(X1, X2)) -> plus(active(X1), X2)
822.52/297.10	  , active(plus(N, 0())) -> mark(N)
822.52/297.10	  , active(plus(N, s(M))) -> mark(s(plus(N, M)))
822.52/297.10	  , active(s(X)) -> s(active(X))
822.52/297.10	  , and(mark(X1), X2) -> mark(and(X1, X2))
822.52/297.10	  , and(ok(X1), ok(X2)) -> ok(and(X1, X2))
822.52/297.10	  , plus(X1, mark(X2)) -> mark(plus(X1, X2))
822.52/297.10	  , plus(mark(X1), X2) -> mark(plus(X1, X2))
822.52/297.10	  , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
822.52/297.10	  , s(mark(X)) -> mark(s(X))
822.52/297.10	  , s(ok(X)) -> ok(s(X))
822.52/297.10	  , proper(and(X1, X2)) -> and(proper(X1), proper(X2))
822.52/297.10	  , proper(tt()) -> ok(tt())
822.52/297.10	  , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
822.52/297.10	  , proper(0()) -> ok(0())
822.52/297.10	  , proper(s(X)) -> s(proper(X))
822.52/297.10	  , top(mark(X)) -> top(proper(X))
822.52/297.10	  , top(ok(X)) -> top(active(X)) }
822.52/297.10	Obligation:
822.52/297.10	  runtime complexity
822.52/297.10	Answer:
822.52/297.10	  YES(?,O(n^1))
822.52/297.10	
822.52/297.10	The problem is match-bounded by 2. The enriched problem is
822.52/297.10	compatible with the following automaton.
822.52/297.10	{ active_0(3) -> 1
822.52/297.10	, active_0(4) -> 1
822.52/297.10	, active_0(6) -> 1
822.52/297.10	, active_0(9) -> 1
822.52/297.10	, active_1(3) -> 15
822.52/297.10	, active_1(4) -> 15
822.52/297.10	, active_1(6) -> 15
822.52/297.10	, active_1(9) -> 15
822.52/297.10	, active_2(14) -> 16
822.52/297.10	, and_0(3, 3) -> 2
822.52/297.10	, and_0(3, 4) -> 2
822.52/297.10	, and_0(3, 6) -> 2
822.52/297.10	, and_0(3, 9) -> 2
822.52/297.10	, and_0(4, 3) -> 2
822.52/297.10	, and_0(4, 4) -> 2
822.52/297.10	, and_0(4, 6) -> 2
822.52/297.10	, and_0(4, 9) -> 2
822.52/297.10	, and_0(6, 3) -> 2
822.52/297.10	, and_0(6, 4) -> 2
822.52/297.10	, and_0(6, 6) -> 2
822.52/297.10	, and_0(6, 9) -> 2
822.52/297.10	, and_0(9, 3) -> 2
822.52/297.10	, and_0(9, 4) -> 2
822.52/297.10	, and_0(9, 6) -> 2
822.52/297.10	, and_0(9, 9) -> 2
822.52/297.10	, and_1(3, 3) -> 11
822.52/297.10	, and_1(3, 4) -> 11
822.52/297.10	, and_1(3, 6) -> 11
822.52/297.10	, and_1(3, 9) -> 11
822.52/297.10	, and_1(4, 3) -> 11
822.52/297.10	, and_1(4, 4) -> 11
822.52/297.10	, and_1(4, 6) -> 11
822.52/297.10	, and_1(4, 9) -> 11
822.52/297.10	, and_1(6, 3) -> 11
822.52/297.10	, and_1(6, 4) -> 11
822.52/297.10	, and_1(6, 6) -> 11
822.52/297.10	, and_1(6, 9) -> 11
822.52/297.10	, and_1(9, 3) -> 11
822.52/297.10	, and_1(9, 4) -> 11
822.52/297.10	, and_1(9, 6) -> 11
822.52/297.10	, and_1(9, 9) -> 11
822.52/297.10	, tt_0() -> 3
822.52/297.10	, tt_1() -> 14
822.52/297.10	, mark_0(3) -> 4
822.52/297.10	, mark_0(4) -> 4
822.52/297.10	, mark_0(6) -> 4
822.52/297.10	, mark_0(9) -> 4
822.52/297.10	, mark_1(11) -> 2
822.52/297.10	, mark_1(11) -> 11
822.52/297.10	, mark_1(12) -> 5
822.52/297.10	, mark_1(12) -> 12
822.52/297.10	, mark_1(13) -> 7
822.52/297.10	, mark_1(13) -> 13
822.52/297.10	, plus_0(3, 3) -> 5
822.52/297.10	, plus_0(3, 4) -> 5
822.52/297.10	, plus_0(3, 6) -> 5
822.52/297.10	, plus_0(3, 9) -> 5
822.52/297.10	, plus_0(4, 3) -> 5
822.52/297.10	, plus_0(4, 4) -> 5
822.52/297.10	, plus_0(4, 6) -> 5
822.52/297.10	, plus_0(4, 9) -> 5
822.52/297.10	, plus_0(6, 3) -> 5
822.52/297.10	, plus_0(6, 4) -> 5
822.52/297.10	, plus_0(6, 6) -> 5
822.52/297.10	, plus_0(6, 9) -> 5
822.52/297.10	, plus_0(9, 3) -> 5
822.52/297.10	, plus_0(9, 4) -> 5
822.52/297.10	, plus_0(9, 6) -> 5
822.52/297.10	, plus_0(9, 9) -> 5
822.52/297.10	, plus_1(3, 3) -> 12
822.52/297.10	, plus_1(3, 4) -> 12
822.52/297.10	, plus_1(3, 6) -> 12
822.52/297.10	, plus_1(3, 9) -> 12
822.52/297.10	, plus_1(4, 3) -> 12
822.52/297.10	, plus_1(4, 4) -> 12
822.52/297.10	, plus_1(4, 6) -> 12
822.52/297.10	, plus_1(4, 9) -> 12
822.52/297.10	, plus_1(6, 3) -> 12
822.52/297.10	, plus_1(6, 4) -> 12
822.52/297.10	, plus_1(6, 6) -> 12
822.52/297.10	, plus_1(6, 9) -> 12
822.52/297.10	, plus_1(9, 3) -> 12
822.52/297.10	, plus_1(9, 4) -> 12
822.52/297.10	, plus_1(9, 6) -> 12
822.52/297.10	, plus_1(9, 9) -> 12
822.52/297.10	, 0_0() -> 6
822.52/297.10	, 0_1() -> 14
822.52/297.10	, s_0(3) -> 7
822.52/297.10	, s_0(4) -> 7
822.52/297.10	, s_0(6) -> 7
822.52/297.10	, s_0(9) -> 7
822.52/297.10	, s_1(3) -> 13
822.52/297.10	, s_1(4) -> 13
822.52/297.10	, s_1(6) -> 13
822.52/297.10	, s_1(9) -> 13
822.52/297.10	, proper_0(3) -> 8
822.52/297.10	, proper_0(4) -> 8
822.52/297.10	, proper_0(6) -> 8
822.52/297.10	, proper_0(9) -> 8
822.52/297.10	, proper_1(3) -> 15
822.52/297.10	, proper_1(4) -> 15
822.52/297.10	, proper_1(6) -> 15
822.52/297.10	, proper_1(9) -> 15
822.52/297.10	, ok_0(3) -> 9
822.52/297.10	, ok_0(4) -> 9
822.52/297.10	, ok_0(6) -> 9
822.52/297.10	, ok_0(9) -> 9
822.52/297.10	, ok_1(11) -> 2
822.52/297.10	, ok_1(11) -> 11
822.52/297.10	, ok_1(12) -> 5
822.52/297.10	, ok_1(12) -> 12
822.52/297.10	, ok_1(13) -> 7
822.52/297.10	, ok_1(13) -> 13
822.52/297.10	, ok_1(14) -> 8
822.52/297.10	, ok_1(14) -> 15
822.52/297.10	, top_0(3) -> 10
822.52/297.10	, top_0(4) -> 10
822.52/297.10	, top_0(6) -> 10
822.52/297.10	, top_0(9) -> 10
822.52/297.10	, top_1(15) -> 10
822.52/297.10	, top_2(16) -> 10 }
822.52/297.10	
822.52/297.10	Hurray, we answered YES(?,O(n^1))
822.52/297.14	EOF