YES(?,O(n^1))
36.85/13.97	YES(?,O(n^1))
36.85/13.97	
36.85/13.97	We are left with following problem, upon which TcT provides the
36.85/13.97	certificate YES(?,O(n^1)).
36.85/13.97	
36.85/13.97	Strict Trs:
36.85/13.97	  { f(X) -> if(X, c(), n__f(n__true()))
36.85/13.97	  , f(X) -> n__f(X)
36.85/13.97	  , if(true(), X, Y) -> X
36.85/13.97	  , if(false(), X, Y) -> activate(Y)
36.85/13.97	  , true() -> n__true()
36.85/13.97	  , activate(X) -> X
36.85/13.97	  , activate(n__f(X)) -> f(activate(X))
36.85/13.97	  , activate(n__true()) -> true() }
36.85/13.97	Obligation:
36.85/13.97	  innermost runtime complexity
36.85/13.97	Answer:
36.85/13.97	  YES(?,O(n^1))
36.85/13.97	
36.85/13.97	Arguments of following rules are not normal-forms:
36.85/13.97	
36.85/13.97	{ if(true(), X, Y) -> X }
36.85/13.97	
36.85/13.97	All above mentioned rules can be savely removed.
36.85/13.97	
36.85/13.97	We are left with following problem, upon which TcT provides the
36.85/13.97	certificate YES(?,O(n^1)).
36.85/13.97	
36.85/13.97	Strict Trs:
36.85/13.97	  { f(X) -> if(X, c(), n__f(n__true()))
36.85/13.97	  , f(X) -> n__f(X)
36.85/13.97	  , if(false(), X, Y) -> activate(Y)
36.85/13.97	  , true() -> n__true()
36.85/13.97	  , activate(X) -> X
36.85/13.97	  , activate(n__f(X)) -> f(activate(X))
36.85/13.97	  , activate(n__true()) -> true() }
36.85/13.97	Obligation:
36.85/13.97	  innermost runtime complexity
36.85/13.97	Answer:
36.85/13.97	  YES(?,O(n^1))
36.85/13.97	
36.85/13.97	The problem is match-bounded by 4. The enriched problem is
36.85/13.97	compatible with the following automaton.
36.85/13.97	{ f_0(3) -> 1
36.85/13.97	, f_0(4) -> 1
36.85/13.97	, f_0(5) -> 1
36.85/13.97	, f_0(7) -> 1
36.85/13.97	, f_1(2) -> 2
36.85/13.97	, f_1(2) -> 8
36.85/13.97	, f_2(12) -> 1
36.85/13.97	, f_2(19) -> 2
36.85/13.97	, f_2(19) -> 8
36.85/13.97	, if_0(3, 3, 3) -> 2
36.85/13.97	, if_0(3, 3, 4) -> 2
36.85/13.97	, if_0(3, 3, 5) -> 2
36.85/13.97	, if_0(3, 3, 7) -> 2
36.85/13.97	, if_0(3, 4, 3) -> 2
36.85/13.97	, if_0(3, 4, 4) -> 2
36.85/13.97	, if_0(3, 4, 5) -> 2
36.85/13.97	, if_0(3, 4, 7) -> 2
36.85/13.97	, if_0(3, 5, 3) -> 2
36.85/13.97	, if_0(3, 5, 4) -> 2
36.85/13.97	, if_0(3, 5, 5) -> 2
36.85/13.97	, if_0(3, 5, 7) -> 2
36.85/13.97	, if_0(3, 7, 3) -> 2
36.85/13.97	, if_0(3, 7, 4) -> 2
36.85/13.97	, if_0(3, 7, 5) -> 2
36.85/13.97	, if_0(3, 7, 7) -> 2
36.85/13.97	, if_0(4, 3, 3) -> 2
36.85/13.97	, if_0(4, 3, 4) -> 2
36.85/13.97	, if_0(4, 3, 5) -> 2
36.85/13.97	, if_0(4, 3, 7) -> 2
36.85/13.97	, if_0(4, 4, 3) -> 2
36.85/13.97	, if_0(4, 4, 4) -> 2
36.85/13.97	, if_0(4, 4, 5) -> 2
36.85/13.97	, if_0(4, 4, 7) -> 2
36.85/13.97	, if_0(4, 5, 3) -> 2
36.85/13.97	, if_0(4, 5, 4) -> 2
36.85/13.97	, if_0(4, 5, 5) -> 2
36.85/13.97	, if_0(4, 5, 7) -> 2
36.85/13.97	, if_0(4, 7, 3) -> 2
36.85/13.97	, if_0(4, 7, 4) -> 2
36.85/13.97	, if_0(4, 7, 5) -> 2
36.85/13.97	, if_0(4, 7, 7) -> 2
36.85/13.97	, if_0(5, 3, 3) -> 2
36.85/13.97	, if_0(5, 3, 4) -> 2
36.85/13.97	, if_0(5, 3, 5) -> 2
36.85/13.97	, if_0(5, 3, 7) -> 2
36.85/13.97	, if_0(5, 4, 3) -> 2
36.85/13.97	, if_0(5, 4, 4) -> 2
36.85/13.97	, if_0(5, 4, 5) -> 2
36.85/13.97	, if_0(5, 4, 7) -> 2
36.85/13.97	, if_0(5, 5, 3) -> 2
36.85/13.97	, if_0(5, 5, 4) -> 2
36.85/13.97	, if_0(5, 5, 5) -> 2
36.85/13.97	, if_0(5, 5, 7) -> 2
36.85/13.97	, if_0(5, 7, 3) -> 2
36.85/13.97	, if_0(5, 7, 4) -> 2
36.85/13.97	, if_0(5, 7, 5) -> 2
36.85/13.97	, if_0(5, 7, 7) -> 2
36.85/13.97	, if_0(7, 3, 3) -> 2
36.85/13.97	, if_0(7, 3, 4) -> 2
36.85/13.97	, if_0(7, 3, 5) -> 2
36.85/13.97	, if_0(7, 3, 7) -> 2
36.85/13.97	, if_0(7, 4, 3) -> 2
36.85/13.97	, if_0(7, 4, 4) -> 2
36.85/13.97	, if_0(7, 4, 5) -> 2
36.85/13.97	, if_0(7, 4, 7) -> 2
36.85/13.97	, if_0(7, 5, 3) -> 2
36.85/13.97	, if_0(7, 5, 4) -> 2
36.85/13.97	, if_0(7, 5, 5) -> 2
36.85/13.97	, if_0(7, 5, 7) -> 2
36.85/13.97	, if_0(7, 7, 3) -> 2
36.85/13.97	, if_0(7, 7, 4) -> 2
36.85/13.97	, if_0(7, 7, 5) -> 2
36.85/13.97	, if_0(7, 7, 7) -> 2
36.85/13.97	, if_1(3, 9, 10) -> 1
36.85/13.97	, if_1(4, 9, 10) -> 1
36.85/13.97	, if_1(5, 9, 10) -> 1
36.85/13.97	, if_1(7, 9, 10) -> 1
36.85/13.97	, if_2(2, 13, 14) -> 2
36.85/13.97	, if_2(2, 13, 14) -> 8
36.85/13.97	, if_3(12, 16, 17) -> 1
36.85/13.97	, if_3(19, 16, 17) -> 2
36.85/13.97	, if_3(19, 16, 17) -> 8
36.85/13.97	, c_0() -> 2
36.85/13.97	, c_0() -> 3
36.85/13.97	, c_0() -> 8
36.85/13.97	, c_1() -> 9
36.85/13.97	, c_2() -> 13
36.85/13.97	, c_3() -> 16
36.85/13.97	, n__f_0(3) -> 2
36.85/13.97	, n__f_0(3) -> 4
36.85/13.97	, n__f_0(3) -> 8
36.85/13.97	, n__f_0(4) -> 2
36.85/13.97	, n__f_0(4) -> 4
36.85/13.97	, n__f_0(4) -> 8
36.85/13.97	, n__f_0(5) -> 2
36.85/13.97	, n__f_0(5) -> 4
36.85/13.97	, n__f_0(5) -> 8
36.85/13.97	, n__f_0(7) -> 2
36.85/13.97	, n__f_0(7) -> 4
36.85/13.97	, n__f_0(7) -> 8
36.85/13.97	, n__f_1(3) -> 1
36.85/13.97	, n__f_1(4) -> 1
36.85/13.97	, n__f_1(5) -> 1
36.85/13.97	, n__f_1(7) -> 1
36.85/13.97	, n__f_1(11) -> 1
36.85/13.97	, n__f_1(11) -> 10
36.85/13.97	, n__f_2(2) -> 2
36.85/13.97	, n__f_2(2) -> 8
36.85/13.97	, n__f_2(15) -> 2
36.85/13.97	, n__f_2(15) -> 8
36.85/13.97	, n__f_2(15) -> 14
36.85/13.97	, n__f_3(12) -> 1
36.85/13.97	, n__f_3(18) -> 17
36.85/13.97	, n__f_3(19) -> 2
36.85/13.97	, n__f_3(19) -> 8
36.85/13.97	, n__true_0() -> 2
36.85/13.97	, n__true_0() -> 5
36.85/13.97	, n__true_0() -> 8
36.85/13.97	, n__true_1() -> 6
36.85/13.97	, n__true_1() -> 11
36.85/13.97	, n__true_1() -> 12
36.85/13.97	, n__true_2() -> 2
36.85/13.97	, n__true_2() -> 8
36.85/13.97	, n__true_2() -> 15
36.85/13.97	, n__true_2() -> 19
36.85/13.97	, n__true_3() -> 12
36.85/13.97	, n__true_3() -> 18
36.85/13.97	, n__true_4() -> 19
36.85/13.97	, true_0() -> 6
36.85/13.97	, true_1() -> 2
36.85/13.97	, true_1() -> 8
36.85/13.97	, true_2() -> 12
36.85/13.97	, true_3() -> 19
36.85/13.97	, false_0() -> 2
36.85/13.97	, false_0() -> 7
36.85/13.97	, false_0() -> 8
36.85/13.97	, activate_0(3) -> 8
36.85/13.97	, activate_0(4) -> 8
36.85/13.97	, activate_0(5) -> 8
36.85/13.97	, activate_0(7) -> 8
36.85/13.97	, activate_1(3) -> 2
36.85/13.97	, activate_1(4) -> 2
36.85/13.97	, activate_1(5) -> 2
36.85/13.97	, activate_1(7) -> 2
36.85/13.97	, activate_1(10) -> 1
36.85/13.97	, activate_1(14) -> 2
36.85/13.97	, activate_1(14) -> 8
36.85/13.97	, activate_2(11) -> 12
36.85/13.97	, activate_2(15) -> 19 }
36.85/13.97	
36.85/13.97	Hurray, we answered YES(?,O(n^1))
36.85/13.99	EOF