YES(?,O(n^1))
835.82/297.08	YES(?,O(n^1))
835.82/297.08	
835.82/297.08	We are left with following problem, upon which TcT provides the
835.82/297.08	certificate YES(?,O(n^1)).
835.82/297.08	
835.82/297.08	Strict Trs:
835.82/297.08	  { active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
835.82/297.08	  , active(U11(tt(), M, N)) -> mark(U12(tt(), M, N))
835.82/297.08	  , active(U12(X1, X2, X3)) -> U12(active(X1), X2, X3)
835.82/297.08	  , active(U12(tt(), M, N)) -> mark(s(plus(N, M)))
835.82/297.08	  , active(s(X)) -> s(active(X))
835.82/297.08	  , active(plus(X1, X2)) -> plus(X1, active(X2))
835.82/297.08	  , active(plus(X1, X2)) -> plus(active(X1), X2)
835.82/297.08	  , active(plus(N, s(M))) -> mark(U11(tt(), M, N))
835.82/297.08	  , active(plus(N, 0())) -> mark(N)
835.82/297.08	  , U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3))
835.82/297.08	  , U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3))
835.82/297.08	  , U12(mark(X1), X2, X3) -> mark(U12(X1, X2, X3))
835.82/297.08	  , U12(ok(X1), ok(X2), ok(X3)) -> ok(U12(X1, X2, X3))
835.82/297.08	  , s(mark(X)) -> mark(s(X))
835.82/297.08	  , s(ok(X)) -> ok(s(X))
835.82/297.08	  , plus(X1, mark(X2)) -> mark(plus(X1, X2))
835.82/297.08	  , plus(mark(X1), X2) -> mark(plus(X1, X2))
835.82/297.08	  , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
835.82/297.08	  , proper(U11(X1, X2, X3)) ->
835.82/297.08	    U11(proper(X1), proper(X2), proper(X3))
835.82/297.08	  , proper(tt()) -> ok(tt())
835.82/297.08	  , proper(U12(X1, X2, X3)) ->
835.82/297.08	    U12(proper(X1), proper(X2), proper(X3))
835.82/297.08	  , proper(s(X)) -> s(proper(X))
835.82/297.08	  , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
835.82/297.08	  , proper(0()) -> ok(0())
835.82/297.08	  , top(mark(X)) -> top(proper(X))
835.82/297.08	  , top(ok(X)) -> top(active(X)) }
835.82/297.08	Obligation:
835.82/297.08	  runtime complexity
835.82/297.08	Answer:
835.82/297.08	  YES(?,O(n^1))
835.82/297.08	
835.82/297.08	The problem is match-bounded by 2. The enriched problem is
835.82/297.08	compatible with the following automaton.
835.82/297.08	{ active_0(3) -> 1
835.82/297.08	, active_0(4) -> 1
835.82/297.08	, active_0(8) -> 1
835.82/297.08	, active_0(10) -> 1
835.82/297.08	, active_1(3) -> 17
835.82/297.08	, active_1(4) -> 17
835.82/297.08	, active_1(8) -> 17
835.82/297.08	, active_1(10) -> 17
835.82/297.08	, active_2(16) -> 18
835.82/297.08	, U11_0(3, 3, 3) -> 2
835.82/297.08	, U11_0(3, 3, 4) -> 2
835.82/297.08	, U11_0(3, 3, 8) -> 2
835.82/297.08	, U11_0(3, 3, 10) -> 2
835.82/297.08	, U11_0(3, 4, 3) -> 2
835.82/297.08	, U11_0(3, 4, 4) -> 2
835.82/297.08	, U11_0(3, 4, 8) -> 2
835.82/297.08	, U11_0(3, 4, 10) -> 2
835.82/297.08	, U11_0(3, 8, 3) -> 2
835.82/297.08	, U11_0(3, 8, 4) -> 2
835.82/297.08	, U11_0(3, 8, 8) -> 2
835.82/297.08	, U11_0(3, 8, 10) -> 2
835.82/297.08	, U11_0(3, 10, 3) -> 2
835.82/297.08	, U11_0(3, 10, 4) -> 2
835.82/297.08	, U11_0(3, 10, 8) -> 2
835.82/297.08	, U11_0(3, 10, 10) -> 2
835.82/297.08	, U11_0(4, 3, 3) -> 2
835.82/297.08	, U11_0(4, 3, 4) -> 2
835.82/297.08	, U11_0(4, 3, 8) -> 2
835.82/297.08	, U11_0(4, 3, 10) -> 2
835.82/297.08	, U11_0(4, 4, 3) -> 2
835.82/297.08	, U11_0(4, 4, 4) -> 2
835.82/297.08	, U11_0(4, 4, 8) -> 2
835.82/297.08	, U11_0(4, 4, 10) -> 2
835.82/297.08	, U11_0(4, 8, 3) -> 2
835.82/297.08	, U11_0(4, 8, 4) -> 2
835.82/297.08	, U11_0(4, 8, 8) -> 2
835.82/297.08	, U11_0(4, 8, 10) -> 2
835.82/297.08	, U11_0(4, 10, 3) -> 2
835.82/297.08	, U11_0(4, 10, 4) -> 2
835.82/297.08	, U11_0(4, 10, 8) -> 2
835.82/297.08	, U11_0(4, 10, 10) -> 2
835.82/297.08	, U11_0(8, 3, 3) -> 2
835.82/297.08	, U11_0(8, 3, 4) -> 2
835.82/297.08	, U11_0(8, 3, 8) -> 2
835.82/297.08	, U11_0(8, 3, 10) -> 2
835.82/297.08	, U11_0(8, 4, 3) -> 2
835.82/297.08	, U11_0(8, 4, 4) -> 2
835.82/297.08	, U11_0(8, 4, 8) -> 2
835.82/297.08	, U11_0(8, 4, 10) -> 2
835.82/297.08	, U11_0(8, 8, 3) -> 2
835.82/297.08	, U11_0(8, 8, 4) -> 2
835.82/297.08	, U11_0(8, 8, 8) -> 2
835.82/297.08	, U11_0(8, 8, 10) -> 2
835.82/297.08	, U11_0(8, 10, 3) -> 2
835.82/297.08	, U11_0(8, 10, 4) -> 2
835.82/297.08	, U11_0(8, 10, 8) -> 2
835.82/297.08	, U11_0(8, 10, 10) -> 2
835.82/297.08	, U11_0(10, 3, 3) -> 2
835.82/297.08	, U11_0(10, 3, 4) -> 2
835.82/297.08	, U11_0(10, 3, 8) -> 2
835.82/297.08	, U11_0(10, 3, 10) -> 2
835.82/297.08	, U11_0(10, 4, 3) -> 2
835.82/297.08	, U11_0(10, 4, 4) -> 2
835.82/297.08	, U11_0(10, 4, 8) -> 2
835.82/297.08	, U11_0(10, 4, 10) -> 2
835.82/297.08	, U11_0(10, 8, 3) -> 2
835.82/297.08	, U11_0(10, 8, 4) -> 2
835.82/297.08	, U11_0(10, 8, 8) -> 2
835.82/297.08	, U11_0(10, 8, 10) -> 2
835.82/297.08	, U11_0(10, 10, 3) -> 2
835.82/297.08	, U11_0(10, 10, 4) -> 2
835.82/297.08	, U11_0(10, 10, 8) -> 2
835.82/297.08	, U11_0(10, 10, 10) -> 2
835.82/297.08	, U11_1(3, 3, 3) -> 12
835.82/297.08	, U11_1(3, 3, 4) -> 12
835.82/297.08	, U11_1(3, 3, 8) -> 12
835.82/297.08	, U11_1(3, 3, 10) -> 12
835.82/297.08	, U11_1(3, 4, 3) -> 12
835.82/297.08	, U11_1(3, 4, 4) -> 12
835.82/297.08	, U11_1(3, 4, 8) -> 12
835.82/297.08	, U11_1(3, 4, 10) -> 12
835.82/297.08	, U11_1(3, 8, 3) -> 12
835.82/297.08	, U11_1(3, 8, 4) -> 12
835.82/297.08	, U11_1(3, 8, 8) -> 12
835.82/297.08	, U11_1(3, 8, 10) -> 12
835.82/297.08	, U11_1(3, 10, 3) -> 12
835.82/297.08	, U11_1(3, 10, 4) -> 12
835.82/297.08	, U11_1(3, 10, 8) -> 12
835.82/297.08	, U11_1(3, 10, 10) -> 12
835.82/297.08	, U11_1(4, 3, 3) -> 12
835.82/297.08	, U11_1(4, 3, 4) -> 12
835.82/297.08	, U11_1(4, 3, 8) -> 12
835.82/297.08	, U11_1(4, 3, 10) -> 12
835.82/297.08	, U11_1(4, 4, 3) -> 12
835.82/297.08	, U11_1(4, 4, 4) -> 12
835.82/297.08	, U11_1(4, 4, 8) -> 12
835.82/297.08	, U11_1(4, 4, 10) -> 12
835.82/297.08	, U11_1(4, 8, 3) -> 12
835.82/297.08	, U11_1(4, 8, 4) -> 12
835.82/297.08	, U11_1(4, 8, 8) -> 12
835.82/297.08	, U11_1(4, 8, 10) -> 12
835.82/297.08	, U11_1(4, 10, 3) -> 12
835.82/297.08	, U11_1(4, 10, 4) -> 12
835.82/297.08	, U11_1(4, 10, 8) -> 12
835.82/297.08	, U11_1(4, 10, 10) -> 12
835.82/297.08	, U11_1(8, 3, 3) -> 12
835.82/297.08	, U11_1(8, 3, 4) -> 12
835.82/297.08	, U11_1(8, 3, 8) -> 12
835.82/297.08	, U11_1(8, 3, 10) -> 12
835.82/297.08	, U11_1(8, 4, 3) -> 12
835.82/297.08	, U11_1(8, 4, 4) -> 12
835.82/297.08	, U11_1(8, 4, 8) -> 12
835.82/297.08	, U11_1(8, 4, 10) -> 12
835.82/297.08	, U11_1(8, 8, 3) -> 12
835.82/297.08	, U11_1(8, 8, 4) -> 12
835.82/297.08	, U11_1(8, 8, 8) -> 12
835.82/297.08	, U11_1(8, 8, 10) -> 12
835.82/297.08	, U11_1(8, 10, 3) -> 12
835.82/297.08	, U11_1(8, 10, 4) -> 12
835.82/297.08	, U11_1(8, 10, 8) -> 12
835.82/297.08	, U11_1(8, 10, 10) -> 12
835.82/297.08	, U11_1(10, 3, 3) -> 12
835.82/297.08	, U11_1(10, 3, 4) -> 12
835.82/297.08	, U11_1(10, 3, 8) -> 12
835.82/297.08	, U11_1(10, 3, 10) -> 12
835.82/297.08	, U11_1(10, 4, 3) -> 12
835.82/297.08	, U11_1(10, 4, 4) -> 12
835.82/297.08	, U11_1(10, 4, 8) -> 12
835.82/297.08	, U11_1(10, 4, 10) -> 12
835.82/297.08	, U11_1(10, 8, 3) -> 12
835.82/297.08	, U11_1(10, 8, 4) -> 12
835.82/297.08	, U11_1(10, 8, 8) -> 12
835.82/297.08	, U11_1(10, 8, 10) -> 12
835.82/297.08	, U11_1(10, 10, 3) -> 12
835.82/297.08	, U11_1(10, 10, 4) -> 12
835.82/297.08	, U11_1(10, 10, 8) -> 12
835.82/297.08	, U11_1(10, 10, 10) -> 12
835.82/297.08	, tt_0() -> 3
835.82/297.08	, tt_1() -> 16
835.82/297.08	, mark_0(3) -> 4
835.82/297.08	, mark_0(4) -> 4
835.82/297.08	, mark_0(8) -> 4
835.82/297.08	, mark_0(10) -> 4
835.82/297.08	, mark_1(12) -> 2
835.82/297.08	, mark_1(12) -> 12
835.82/297.08	, mark_1(13) -> 5
835.82/297.08	, mark_1(13) -> 13
835.82/297.08	, mark_1(14) -> 6
835.82/297.08	, mark_1(14) -> 14
835.82/297.08	, mark_1(15) -> 7
835.82/297.08	, mark_1(15) -> 15
835.82/297.08	, U12_0(3, 3, 3) -> 5
835.82/297.08	, U12_0(3, 3, 4) -> 5
835.82/297.08	, U12_0(3, 3, 8) -> 5
835.82/297.08	, U12_0(3, 3, 10) -> 5
835.82/297.08	, U12_0(3, 4, 3) -> 5
835.82/297.08	, U12_0(3, 4, 4) -> 5
835.82/297.08	, U12_0(3, 4, 8) -> 5
835.82/297.08	, U12_0(3, 4, 10) -> 5
835.82/297.08	, U12_0(3, 8, 3) -> 5
835.82/297.08	, U12_0(3, 8, 4) -> 5
835.82/297.08	, U12_0(3, 8, 8) -> 5
835.82/297.08	, U12_0(3, 8, 10) -> 5
835.82/297.08	, U12_0(3, 10, 3) -> 5
835.82/297.08	, U12_0(3, 10, 4) -> 5
835.82/297.08	, U12_0(3, 10, 8) -> 5
835.82/297.08	, U12_0(3, 10, 10) -> 5
835.82/297.08	, U12_0(4, 3, 3) -> 5
835.82/297.08	, U12_0(4, 3, 4) -> 5
835.82/297.08	, U12_0(4, 3, 8) -> 5
835.82/297.08	, U12_0(4, 3, 10) -> 5
835.82/297.08	, U12_0(4, 4, 3) -> 5
835.82/297.08	, U12_0(4, 4, 4) -> 5
835.82/297.08	, U12_0(4, 4, 8) -> 5
835.82/297.08	, U12_0(4, 4, 10) -> 5
835.82/297.08	, U12_0(4, 8, 3) -> 5
835.82/297.08	, U12_0(4, 8, 4) -> 5
835.82/297.08	, U12_0(4, 8, 8) -> 5
835.82/297.08	, U12_0(4, 8, 10) -> 5
835.82/297.08	, U12_0(4, 10, 3) -> 5
835.82/297.08	, U12_0(4, 10, 4) -> 5
835.82/297.08	, U12_0(4, 10, 8) -> 5
835.82/297.08	, U12_0(4, 10, 10) -> 5
835.82/297.08	, U12_0(8, 3, 3) -> 5
835.82/297.08	, U12_0(8, 3, 4) -> 5
835.82/297.08	, U12_0(8, 3, 8) -> 5
835.82/297.08	, U12_0(8, 3, 10) -> 5
835.82/297.08	, U12_0(8, 4, 3) -> 5
835.82/297.08	, U12_0(8, 4, 4) -> 5
835.82/297.08	, U12_0(8, 4, 8) -> 5
835.82/297.08	, U12_0(8, 4, 10) -> 5
835.82/297.08	, U12_0(8, 8, 3) -> 5
835.82/297.08	, U12_0(8, 8, 4) -> 5
835.82/297.08	, U12_0(8, 8, 8) -> 5
835.82/297.08	, U12_0(8, 8, 10) -> 5
835.82/297.08	, U12_0(8, 10, 3) -> 5
835.82/297.08	, U12_0(8, 10, 4) -> 5
835.82/297.08	, U12_0(8, 10, 8) -> 5
835.82/297.08	, U12_0(8, 10, 10) -> 5
835.82/297.08	, U12_0(10, 3, 3) -> 5
835.82/297.08	, U12_0(10, 3, 4) -> 5
835.82/297.08	, U12_0(10, 3, 8) -> 5
835.82/297.08	, U12_0(10, 3, 10) -> 5
835.82/297.08	, U12_0(10, 4, 3) -> 5
835.82/297.08	, U12_0(10, 4, 4) -> 5
835.82/297.08	, U12_0(10, 4, 8) -> 5
835.82/297.08	, U12_0(10, 4, 10) -> 5
835.82/297.08	, U12_0(10, 8, 3) -> 5
835.82/297.08	, U12_0(10, 8, 4) -> 5
835.82/297.08	, U12_0(10, 8, 8) -> 5
835.82/297.08	, U12_0(10, 8, 10) -> 5
835.82/297.08	, U12_0(10, 10, 3) -> 5
835.82/297.08	, U12_0(10, 10, 4) -> 5
835.82/297.08	, U12_0(10, 10, 8) -> 5
835.82/297.08	, U12_0(10, 10, 10) -> 5
835.82/297.08	, U12_1(3, 3, 3) -> 13
835.82/297.08	, U12_1(3, 3, 4) -> 13
835.82/297.08	, U12_1(3, 3, 8) -> 13
835.82/297.08	, U12_1(3, 3, 10) -> 13
835.82/297.08	, U12_1(3, 4, 3) -> 13
835.82/297.08	, U12_1(3, 4, 4) -> 13
835.82/297.08	, U12_1(3, 4, 8) -> 13
835.82/297.08	, U12_1(3, 4, 10) -> 13
835.82/297.08	, U12_1(3, 8, 3) -> 13
835.82/297.08	, U12_1(3, 8, 4) -> 13
835.82/297.08	, U12_1(3, 8, 8) -> 13
835.82/297.08	, U12_1(3, 8, 10) -> 13
835.82/297.08	, U12_1(3, 10, 3) -> 13
835.82/297.08	, U12_1(3, 10, 4) -> 13
835.82/297.08	, U12_1(3, 10, 8) -> 13
835.82/297.08	, U12_1(3, 10, 10) -> 13
835.82/297.08	, U12_1(4, 3, 3) -> 13
835.82/297.08	, U12_1(4, 3, 4) -> 13
835.82/297.08	, U12_1(4, 3, 8) -> 13
835.82/297.08	, U12_1(4, 3, 10) -> 13
835.82/297.08	, U12_1(4, 4, 3) -> 13
835.82/297.08	, U12_1(4, 4, 4) -> 13
835.82/297.08	, U12_1(4, 4, 8) -> 13
835.82/297.08	, U12_1(4, 4, 10) -> 13
835.82/297.08	, U12_1(4, 8, 3) -> 13
835.82/297.08	, U12_1(4, 8, 4) -> 13
835.82/297.08	, U12_1(4, 8, 8) -> 13
835.82/297.08	, U12_1(4, 8, 10) -> 13
835.82/297.08	, U12_1(4, 10, 3) -> 13
835.82/297.08	, U12_1(4, 10, 4) -> 13
835.82/297.08	, U12_1(4, 10, 8) -> 13
835.82/297.08	, U12_1(4, 10, 10) -> 13
835.82/297.08	, U12_1(8, 3, 3) -> 13
835.82/297.08	, U12_1(8, 3, 4) -> 13
835.82/297.08	, U12_1(8, 3, 8) -> 13
835.82/297.08	, U12_1(8, 3, 10) -> 13
835.82/297.08	, U12_1(8, 4, 3) -> 13
835.82/297.08	, U12_1(8, 4, 4) -> 13
835.82/297.08	, U12_1(8, 4, 8) -> 13
835.82/297.08	, U12_1(8, 4, 10) -> 13
835.82/297.08	, U12_1(8, 8, 3) -> 13
835.82/297.08	, U12_1(8, 8, 4) -> 13
835.82/297.08	, U12_1(8, 8, 8) -> 13
835.82/297.08	, U12_1(8, 8, 10) -> 13
835.82/297.08	, U12_1(8, 10, 3) -> 13
835.82/297.08	, U12_1(8, 10, 4) -> 13
835.82/297.08	, U12_1(8, 10, 8) -> 13
835.82/297.08	, U12_1(8, 10, 10) -> 13
835.82/297.08	, U12_1(10, 3, 3) -> 13
835.82/297.08	, U12_1(10, 3, 4) -> 13
835.82/297.08	, U12_1(10, 3, 8) -> 13
835.82/297.08	, U12_1(10, 3, 10) -> 13
835.82/297.08	, U12_1(10, 4, 3) -> 13
835.82/297.08	, U12_1(10, 4, 4) -> 13
835.82/297.08	, U12_1(10, 4, 8) -> 13
835.82/297.08	, U12_1(10, 4, 10) -> 13
835.82/297.08	, U12_1(10, 8, 3) -> 13
835.82/297.08	, U12_1(10, 8, 4) -> 13
835.82/297.08	, U12_1(10, 8, 8) -> 13
835.82/297.08	, U12_1(10, 8, 10) -> 13
835.82/297.08	, U12_1(10, 10, 3) -> 13
835.82/297.08	, U12_1(10, 10, 4) -> 13
835.82/297.08	, U12_1(10, 10, 8) -> 13
835.82/297.08	, U12_1(10, 10, 10) -> 13
835.82/297.08	, s_0(3) -> 6
835.82/297.08	, s_0(4) -> 6
835.82/297.08	, s_0(8) -> 6
835.82/297.08	, s_0(10) -> 6
835.82/297.08	, s_1(3) -> 14
835.82/297.08	, s_1(4) -> 14
835.82/297.08	, s_1(8) -> 14
835.82/297.08	, s_1(10) -> 14
835.82/297.08	, plus_0(3, 3) -> 7
835.82/297.08	, plus_0(3, 4) -> 7
835.82/297.08	, plus_0(3, 8) -> 7
835.82/297.08	, plus_0(3, 10) -> 7
835.82/297.08	, plus_0(4, 3) -> 7
835.82/297.08	, plus_0(4, 4) -> 7
835.82/297.08	, plus_0(4, 8) -> 7
835.82/297.08	, plus_0(4, 10) -> 7
835.82/297.08	, plus_0(8, 3) -> 7
835.82/297.08	, plus_0(8, 4) -> 7
835.82/297.08	, plus_0(8, 8) -> 7
835.82/297.08	, plus_0(8, 10) -> 7
835.82/297.08	, plus_0(10, 3) -> 7
835.82/297.08	, plus_0(10, 4) -> 7
835.82/297.08	, plus_0(10, 8) -> 7
835.82/297.08	, plus_0(10, 10) -> 7
835.82/297.08	, plus_1(3, 3) -> 15
835.82/297.08	, plus_1(3, 4) -> 15
835.82/297.08	, plus_1(3, 8) -> 15
835.82/297.08	, plus_1(3, 10) -> 15
835.82/297.08	, plus_1(4, 3) -> 15
835.82/297.08	, plus_1(4, 4) -> 15
835.82/297.08	, plus_1(4, 8) -> 15
835.82/297.08	, plus_1(4, 10) -> 15
835.82/297.08	, plus_1(8, 3) -> 15
835.82/297.08	, plus_1(8, 4) -> 15
835.82/297.08	, plus_1(8, 8) -> 15
835.82/297.08	, plus_1(8, 10) -> 15
835.82/297.08	, plus_1(10, 3) -> 15
835.82/297.08	, plus_1(10, 4) -> 15
835.82/297.08	, plus_1(10, 8) -> 15
835.82/297.08	, plus_1(10, 10) -> 15
835.82/297.08	, 0_0() -> 8
835.82/297.08	, 0_1() -> 16
835.82/297.08	, proper_0(3) -> 9
835.82/297.08	, proper_0(4) -> 9
835.82/297.08	, proper_0(8) -> 9
835.82/297.08	, proper_0(10) -> 9
835.82/297.08	, proper_1(3) -> 17
835.82/297.08	, proper_1(4) -> 17
835.82/297.08	, proper_1(8) -> 17
835.82/297.08	, proper_1(10) -> 17
835.82/297.08	, ok_0(3) -> 10
835.82/297.08	, ok_0(4) -> 10
835.82/297.08	, ok_0(8) -> 10
835.82/297.08	, ok_0(10) -> 10
835.82/297.08	, ok_1(12) -> 2
835.82/297.08	, ok_1(12) -> 12
835.82/297.08	, ok_1(13) -> 5
835.82/297.08	, ok_1(13) -> 13
835.82/297.08	, ok_1(14) -> 6
835.82/297.08	, ok_1(14) -> 14
835.82/297.08	, ok_1(15) -> 7
835.82/297.08	, ok_1(15) -> 15
835.82/297.08	, ok_1(16) -> 9
835.82/297.08	, ok_1(16) -> 17
835.82/297.08	, top_0(3) -> 11
835.82/297.08	, top_0(4) -> 11
835.82/297.08	, top_0(8) -> 11
835.82/297.08	, top_0(10) -> 11
835.82/297.08	, top_1(17) -> 11
835.82/297.08	, top_2(18) -> 11 }
835.82/297.08	
835.82/297.08	Hurray, we answered YES(?,O(n^1))
835.82/297.15	EOF