YES(?,O(n^1))
5.97/1.79	YES(?,O(n^1))
5.97/1.79	
5.97/1.79	We are left with following problem, upon which TcT provides the
5.97/1.79	certificate YES(?,O(n^1)).
5.97/1.79	
5.97/1.79	Strict Trs:
5.97/1.79	  { f(X) -> n__f(X)
5.97/1.79	  , f(0()) -> cons(0(), n__f(s(0())))
5.97/1.79	  , f(s(0())) -> f(p(s(0())))
5.97/1.79	  , p(s(X)) -> X
5.97/1.79	  , activate(X) -> X
5.97/1.79	  , activate(n__f(X)) -> f(X) }
5.97/1.79	Obligation:
5.97/1.79	  runtime complexity
5.97/1.79	Answer:
5.97/1.79	  YES(?,O(n^1))
5.97/1.79	
5.97/1.79	The input is overlay and right-linear. Switching to innermost
5.97/1.79	rewriting.
5.97/1.79	
5.97/1.79	We are left with following problem, upon which TcT provides the
5.97/1.79	certificate YES(?,O(n^1)).
5.97/1.79	
5.97/1.79	Strict Trs:
5.97/1.79	  { f(X) -> n__f(X)
5.97/1.79	  , f(0()) -> cons(0(), n__f(s(0())))
5.97/1.79	  , f(s(0())) -> f(p(s(0())))
5.97/1.79	  , p(s(X)) -> X
5.97/1.79	  , activate(X) -> X
5.97/1.79	  , activate(n__f(X)) -> f(X) }
5.97/1.79	Obligation:
5.97/1.79	  innermost runtime complexity
5.97/1.79	Answer:
5.97/1.79	  YES(?,O(n^1))
5.97/1.79	
5.97/1.79	The problem is match-bounded by 2. The enriched problem is
5.97/1.79	compatible with the following automaton.
5.97/1.79	{ f_0(2) -> 1
5.97/1.79	, f_1(2) -> 1
5.97/1.79	, f_1(7) -> 1
5.97/1.79	, 0_0() -> 1
5.97/1.79	, 0_0() -> 2
5.97/1.79	, 0_1() -> 3
5.97/1.79	, 0_1() -> 6
5.97/1.79	, 0_1() -> 7
5.97/1.79	, 0_2() -> 8
5.97/1.79	, 0_2() -> 11
5.97/1.79	, cons_0(2, 2) -> 1
5.97/1.79	, cons_0(2, 2) -> 2
5.97/1.79	, cons_1(3, 4) -> 1
5.97/1.79	, cons_2(8, 9) -> 1
5.97/1.79	, n__f_0(2) -> 1
5.97/1.79	, n__f_0(2) -> 2
5.97/1.79	, n__f_1(2) -> 1
5.97/1.79	, n__f_1(5) -> 4
5.97/1.79	, n__f_2(2) -> 1
5.97/1.79	, n__f_2(7) -> 1
5.97/1.79	, n__f_2(10) -> 9
5.97/1.79	, s_0(2) -> 1
5.97/1.79	, s_0(2) -> 2
5.97/1.79	, s_1(6) -> 5
5.97/1.79	, s_2(11) -> 10
5.97/1.79	, p_0(2) -> 1
5.97/1.79	, p_1(5) -> 7
5.97/1.79	, activate_0(2) -> 1 }
5.97/1.79	
5.97/1.79	Hurray, we answered YES(?,O(n^1))
6.20/1.80	EOF