YES(?,O(n^1))
12.02/6.73	YES(?,O(n^1))
12.02/6.73	
12.02/6.73	We are left with following problem, upon which TcT provides the
12.02/6.73	certificate YES(?,O(n^1)).
12.02/6.73	
12.02/6.73	Strict Trs:
12.02/6.73	  { f(X) -> n__f(X)
12.02/6.73	  , f(f(a())) -> f(g(n__f(a())))
12.02/6.73	  , activate(X) -> X
12.02/6.73	  , activate(n__f(X)) -> f(X) }
12.02/6.73	Obligation:
12.02/6.73	  derivational complexity
12.02/6.73	Answer:
12.02/6.73	  YES(?,O(n^1))
12.02/6.73	
12.02/6.73	The problem is match-bounded by 2. The enriched problem is
12.02/6.73	compatible with the following automaton.
12.02/6.73	{ f_0(1) -> 1
12.02/6.73	, f_0(1) -> 5
12.02/6.73	, f_0(2) -> 1
12.02/6.73	, f_0(2) -> 5
12.02/6.73	, f_0(3) -> 1
12.02/6.73	, f_0(3) -> 5
12.02/6.73	, f_0(4) -> 1
12.02/6.73	, f_0(4) -> 5
12.02/6.73	, f_0(5) -> 1
12.02/6.73	, f_0(5) -> 5
12.02/6.73	, f_1(1) -> 5
12.02/6.73	, f_1(2) -> 5
12.02/6.73	, f_1(3) -> 5
12.02/6.73	, f_1(4) -> 5
12.02/6.73	, f_1(5) -> 5
12.02/6.73	, f_1(6) -> 1
12.02/6.73	, f_1(6) -> 5
12.02/6.73	, a_0() -> 2
12.02/6.73	, a_0() -> 5
12.02/6.73	, a_1() -> 8
12.02/6.73	, g_0(1) -> 3
12.02/6.73	, g_0(1) -> 5
12.02/6.73	, g_0(2) -> 3
12.02/6.73	, g_0(2) -> 5
12.02/6.73	, g_0(3) -> 3
12.02/6.73	, g_0(3) -> 5
12.02/6.73	, g_0(4) -> 3
12.02/6.73	, g_0(4) -> 5
12.02/6.73	, g_0(5) -> 3
12.02/6.73	, g_0(5) -> 5
12.02/6.73	, g_1(7) -> 6
12.02/6.73	, n__f_0(1) -> 4
12.02/6.73	, n__f_0(1) -> 5
12.02/6.73	, n__f_0(2) -> 4
12.02/6.73	, n__f_0(2) -> 5
12.02/6.73	, n__f_0(3) -> 4
12.02/6.73	, n__f_0(3) -> 5
12.02/6.73	, n__f_0(4) -> 4
12.02/6.73	, n__f_0(4) -> 5
12.02/6.73	, n__f_0(5) -> 4
12.02/6.73	, n__f_0(5) -> 5
12.02/6.73	, n__f_1(1) -> 1
12.02/6.73	, n__f_1(1) -> 5
12.02/6.73	, n__f_1(2) -> 1
12.02/6.73	, n__f_1(2) -> 5
12.02/6.73	, n__f_1(3) -> 1
12.02/6.73	, n__f_1(3) -> 5
12.02/6.73	, n__f_1(4) -> 1
12.02/6.73	, n__f_1(4) -> 5
12.02/6.73	, n__f_1(5) -> 1
12.02/6.73	, n__f_1(5) -> 5
12.02/6.73	, n__f_1(8) -> 7
12.02/6.73	, n__f_2(1) -> 5
12.02/6.73	, n__f_2(2) -> 5
12.02/6.73	, n__f_2(3) -> 5
12.02/6.73	, n__f_2(4) -> 5
12.02/6.73	, n__f_2(5) -> 5
12.02/6.73	, n__f_2(6) -> 1
12.02/6.73	, n__f_2(6) -> 5
12.02/6.73	, activate_0(1) -> 5
12.02/6.73	, activate_0(2) -> 5
12.02/6.73	, activate_0(3) -> 5
12.02/6.73	, activate_0(4) -> 5
12.02/6.73	, activate_0(5) -> 5 }
12.02/6.73	
12.02/6.73	Hurray, we answered YES(?,O(n^1))
12.02/6.75	EOF