YES(?,O(n^1))
0.00/0.47	YES(?,O(n^1))
0.00/0.47	
0.00/0.47	We are left with following problem, upon which TcT provides the
0.00/0.47	certificate YES(?,O(n^1)).
0.00/0.47	
0.00/0.47	Strict Trs:
0.00/0.47	  { f(X) -> n__f(X)
0.00/0.47	  , f(f(X)) -> c(n__f(n__g(n__f(X))))
0.00/0.47	  , c(X) -> d(activate(X))
0.00/0.47	  , d(X) -> n__d(X)
0.00/0.47	  , activate(X) -> X
0.00/0.47	  , activate(n__f(X)) -> f(activate(X))
0.00/0.47	  , activate(n__g(X)) -> g(X)
0.00/0.47	  , activate(n__d(X)) -> d(X)
0.00/0.47	  , h(X) -> c(n__d(X))
0.00/0.47	  , g(X) -> n__g(X) }
0.00/0.47	Obligation:
0.00/0.47	  innermost runtime complexity
0.00/0.47	Answer:
0.00/0.47	  YES(?,O(n^1))
0.00/0.47	
0.00/0.47	Arguments of following rules are not normal-forms:
0.00/0.47	
0.00/0.47	{ f(f(X)) -> c(n__f(n__g(n__f(X)))) }
0.00/0.47	
0.00/0.47	All above mentioned rules can be savely removed.
0.00/0.47	
0.00/0.47	We are left with following problem, upon which TcT provides the
0.00/0.47	certificate YES(?,O(n^1)).
0.00/0.47	
0.00/0.47	Strict Trs:
0.00/0.47	  { f(X) -> n__f(X)
0.00/0.47	  , c(X) -> d(activate(X))
0.00/0.47	  , d(X) -> n__d(X)
0.00/0.47	  , activate(X) -> X
0.00/0.47	  , activate(n__f(X)) -> f(activate(X))
0.00/0.47	  , activate(n__g(X)) -> g(X)
0.00/0.47	  , activate(n__d(X)) -> d(X)
0.00/0.47	  , h(X) -> c(n__d(X))
0.00/0.47	  , g(X) -> n__g(X) }
0.00/0.47	Obligation:
0.00/0.47	  innermost runtime complexity
0.00/0.47	Answer:
0.00/0.47	  YES(?,O(n^1))
0.00/0.47	
0.00/0.47	The problem is match-bounded by 4. The enriched problem is
0.00/0.47	compatible with the following automaton.
0.00/0.47	{ f_0(2) -> 1
0.00/0.47	, f_0(2) -> 4
0.00/0.47	, f_1(3) -> 1
0.00/0.47	, f_1(3) -> 3
0.00/0.47	, f_1(3) -> 4
0.00/0.47	, f_1(3) -> 6
0.00/0.47	, f_1(6) -> 5
0.00/0.47	, f_2(5) -> 4
0.00/0.47	, f_3(6) -> 4
0.00/0.47	, f_3(6) -> 6
0.00/0.47	, c_0(2) -> 1
0.00/0.47	, c_0(2) -> 4
0.00/0.47	, c_1(1) -> 1
0.00/0.47	, c_1(1) -> 4
0.00/0.47	, n__f_0(2) -> 1
0.00/0.47	, n__f_0(2) -> 2
0.00/0.47	, n__f_0(2) -> 3
0.00/0.47	, n__f_0(2) -> 4
0.00/0.47	, n__f_0(2) -> 5
0.00/0.47	, n__f_0(2) -> 6
0.00/0.47	, n__f_1(2) -> 1
0.00/0.47	, n__f_1(2) -> 4
0.00/0.47	, n__f_2(3) -> 1
0.00/0.47	, n__f_2(3) -> 3
0.00/0.47	, n__f_2(3) -> 4
0.00/0.47	, n__f_2(3) -> 6
0.00/0.47	, n__f_2(6) -> 5
0.00/0.47	, n__f_3(5) -> 4
0.00/0.47	, n__f_4(6) -> 4
0.00/0.47	, n__f_4(6) -> 6
0.00/0.47	, n__g_0(2) -> 1
0.00/0.47	, n__g_0(2) -> 2
0.00/0.47	, n__g_0(2) -> 3
0.00/0.47	, n__g_0(2) -> 4
0.00/0.47	, n__g_0(2) -> 5
0.00/0.47	, n__g_0(2) -> 6
0.00/0.47	, n__g_1(2) -> 1
0.00/0.47	, n__g_1(2) -> 4
0.00/0.47	, n__g_2(2) -> 1
0.00/0.47	, n__g_2(2) -> 3
0.00/0.47	, n__g_2(2) -> 4
0.00/0.47	, n__g_2(2) -> 5
0.00/0.47	, n__g_2(2) -> 6
0.00/0.47	, n__g_3(2) -> 4
0.00/0.47	, n__g_4(2) -> 4
0.00/0.47	, n__g_4(2) -> 6
0.00/0.47	, d_0(2) -> 1
0.00/0.47	, d_0(2) -> 4
0.00/0.47	, d_1(2) -> 1
0.00/0.47	, d_1(2) -> 3
0.00/0.47	, d_1(2) -> 4
0.00/0.47	, d_1(2) -> 5
0.00/0.47	, d_1(2) -> 6
0.00/0.47	, d_1(3) -> 1
0.00/0.47	, d_1(3) -> 4
0.00/0.47	, d_2(2) -> 4
0.00/0.47	, d_2(4) -> 1
0.00/0.47	, d_2(4) -> 4
0.00/0.47	, d_3(2) -> 4
0.00/0.47	, d_3(2) -> 6
0.00/0.47	, d_3(3) -> 4
0.00/0.47	, d_3(4) -> 4
0.00/0.47	, activate_0(2) -> 1
0.00/0.47	, activate_0(2) -> 4
0.00/0.47	, activate_1(2) -> 3
0.00/0.47	, activate_1(2) -> 6
0.00/0.47	, activate_2(1) -> 4
0.00/0.47	, activate_2(2) -> 5
0.00/0.47	, activate_3(3) -> 6
0.00/0.47	, h_0(2) -> 1
0.00/0.47	, h_0(2) -> 4
0.00/0.47	, n__d_0(2) -> 1
0.00/0.47	, n__d_0(2) -> 2
0.00/0.47	, n__d_0(2) -> 3
0.00/0.47	, n__d_0(2) -> 4
0.00/0.47	, n__d_0(2) -> 5
0.00/0.47	, n__d_0(2) -> 6
0.00/0.47	, n__d_1(2) -> 1
0.00/0.47	, n__d_1(2) -> 4
0.00/0.47	, n__d_2(2) -> 1
0.00/0.47	, n__d_2(2) -> 3
0.00/0.47	, n__d_2(2) -> 4
0.00/0.47	, n__d_2(2) -> 5
0.00/0.47	, n__d_2(2) -> 6
0.00/0.47	, n__d_2(3) -> 1
0.00/0.47	, n__d_2(3) -> 4
0.00/0.47	, n__d_3(2) -> 4
0.00/0.47	, n__d_3(4) -> 1
0.00/0.47	, n__d_3(4) -> 4
0.00/0.47	, n__d_4(2) -> 4
0.00/0.47	, n__d_4(2) -> 6
0.00/0.47	, n__d_4(3) -> 4
0.00/0.47	, n__d_4(4) -> 4
0.00/0.47	, g_0(2) -> 1
0.00/0.47	, g_0(2) -> 4
0.00/0.47	, g_1(2) -> 1
0.00/0.47	, g_1(2) -> 3
0.00/0.47	, g_1(2) -> 4
0.00/0.47	, g_1(2) -> 5
0.00/0.47	, g_1(2) -> 6
0.00/0.47	, g_2(2) -> 4
0.00/0.47	, g_3(2) -> 4
0.00/0.47	, g_3(2) -> 6 }
0.00/0.47	
0.00/0.47	Hurray, we answered YES(?,O(n^1))
0.00/0.47	EOF