YES(?,O(n^1))
0.00/0.45	YES(?,O(n^1))
0.00/0.45	
0.00/0.45	We are left with following problem, upon which TcT provides the
0.00/0.45	certificate YES(?,O(n^1)).
0.00/0.45	
0.00/0.45	Strict Trs:
0.00/0.45	  { addlist(Cons(x, xs'), Cons(S(0()), xs)) ->
0.00/0.45	    Cons(S(x), addlist(xs', xs))
0.00/0.45	  , addlist(Cons(S(0()), xs'), Cons(x, xs)) ->
0.00/0.45	    Cons(S(x), addlist(xs', xs))
0.00/0.45	  , addlist(Nil(), ys) -> Nil()
0.00/0.45	  , notEmpty(Cons(x, xs)) -> True()
0.00/0.45	  , notEmpty(Nil()) -> False()
0.00/0.45	  , goal(xs, ys) -> addlist(xs, ys) }
0.00/0.45	Obligation:
0.00/0.45	  innermost runtime complexity
0.00/0.45	Answer:
0.00/0.45	  YES(?,O(n^1))
0.00/0.45	
0.00/0.45	The input was oriented with the instance of 'Small Polynomial Path
0.00/0.45	Order (PS,1-bounded)' as induced by the safe mapping
0.00/0.45	
0.00/0.45	 safe(addlist) = {1}, safe(Cons) = {1, 2}, safe(S) = {1},
0.00/0.45	 safe(0) = {}, safe(Nil) = {}, safe(notEmpty) = {}, safe(True) = {},
0.00/0.45	 safe(False) = {}, safe(goal) = {1}
0.00/0.45	
0.00/0.45	and precedence
0.00/0.45	
0.00/0.45	 notEmpty > addlist, goal > addlist, notEmpty ~ goal .
0.00/0.45	
0.00/0.45	Following symbols are considered recursive:
0.00/0.45	
0.00/0.45	 {addlist}
0.00/0.45	
0.00/0.45	The recursion depth is 1.
0.00/0.45	
0.00/0.45	For your convenience, here are the satisfied ordering constraints:
0.00/0.45	
0.00/0.45	  addlist(Cons(; S(; 0()),  xs); Cons(; x,  xs')) > Cons(; S(; x),  addlist(xs; xs'))
0.00/0.45	                                                                                     
0.00/0.45	  addlist(Cons(; x,  xs); Cons(; S(; 0()),  xs')) > Cons(; S(; x),  addlist(xs; xs'))
0.00/0.45	                                                                                     
0.00/0.45	                               addlist(ys; Nil()) > Nil()                            
0.00/0.45	                                                                                     
0.00/0.45	                        notEmpty(Cons(; x,  xs);) > True()                           
0.00/0.45	                                                                                     
0.00/0.45	                                 notEmpty(Nil();) > False()                          
0.00/0.45	                                                                                     
0.00/0.45	                                     goal(ys; xs) > addlist(ys; xs)                  
0.00/0.45	                                                                                     
0.00/0.45	
0.00/0.45	Hurray, we answered YES(?,O(n^1))
0.00/0.45	EOF