YES(?,O(1))
0.00/0.15	YES(?,O(1))
0.00/0.15	
0.00/0.15	We are left with following problem, upon which TcT provides the
0.00/0.15	certificate YES(?,O(1)).
0.00/0.15	
0.00/0.15	Strict Trs:
0.00/0.15	  { terms(N) -> cons(recip(sqr(N)))
0.00/0.15	  , sqr(0()) -> 0()
0.00/0.15	  , sqr(s()) -> s()
0.00/0.15	  , dbl(0()) -> 0()
0.00/0.15	  , dbl(s()) -> s()
0.00/0.15	  , add(0(), X) -> X
0.00/0.15	  , add(s(), Y) -> s()
0.00/0.15	  , first(0(), X) -> nil()
0.00/0.15	  , first(s(), cons(Y)) -> cons(Y) }
0.00/0.15	Obligation:
0.00/0.15	  runtime complexity
0.00/0.15	Answer:
0.00/0.15	  YES(?,O(1))
0.00/0.15	
0.00/0.15	The input is overlay and right-linear. Switching to innermost
0.00/0.15	rewriting.
0.00/0.15	
0.00/0.15	We are left with following problem, upon which TcT provides the
0.00/0.15	certificate YES(?,O(1)).
0.00/0.15	
0.00/0.15	Strict Trs:
0.00/0.15	  { terms(N) -> cons(recip(sqr(N)))
0.00/0.15	  , sqr(0()) -> 0()
0.00/0.15	  , sqr(s()) -> s()
0.00/0.15	  , dbl(0()) -> 0()
0.00/0.15	  , dbl(s()) -> s()
0.00/0.15	  , add(0(), X) -> X
0.00/0.15	  , add(s(), Y) -> s()
0.00/0.15	  , first(0(), X) -> nil()
0.00/0.15	  , first(s(), cons(Y)) -> cons(Y) }
0.00/0.15	Obligation:
0.00/0.15	  innermost runtime complexity
0.00/0.15	Answer:
0.00/0.15	  YES(?,O(1))
0.00/0.15	
0.00/0.15	The input was oriented with the instance of 'Small Polynomial Path
0.00/0.15	Order (PS,0-bounded)' as induced by the safe mapping
0.00/0.15	
0.00/0.15	 safe(terms) = {1}, safe(cons) = {1}, safe(recip) = {1},
0.00/0.15	 safe(sqr) = {1}, safe(0) = {}, safe(s) = {}, safe(dbl) = {},
0.00/0.15	 safe(add) = {}, safe(first) = {1}, safe(nil) = {}
0.00/0.15	
0.00/0.15	and precedence
0.00/0.15	
0.00/0.15	 terms > sqr, terms > add, dbl > sqr, dbl > add, first > sqr,
0.00/0.15	 first > add, terms ~ dbl, terms ~ first, sqr ~ add, dbl ~ first .
0.00/0.15	
0.00/0.15	Following symbols are considered recursive:
0.00/0.15	
0.00/0.15	 {}
0.00/0.15	
0.00/0.15	The recursion depth is 0.
0.00/0.15	
0.00/0.15	For your convenience, here are the satisfied ordering constraints:
0.00/0.15	
0.00/0.15	             terms(; N) > cons(; recip(; sqr(; N)))
0.00/0.15	                                                   
0.00/0.15	             sqr(; 0()) > 0()                      
0.00/0.15	                                                   
0.00/0.15	             sqr(; s()) > s()                      
0.00/0.15	                                                   
0.00/0.15	              dbl(0();) > 0()                      
0.00/0.15	                                                   
0.00/0.15	              dbl(s();) > s()                      
0.00/0.15	                                                   
0.00/0.15	          add(0(),  X;) > X                        
0.00/0.15	                                                   
0.00/0.15	          add(s(),  Y;) > s()                      
0.00/0.15	                                                   
0.00/0.15	          first(X; 0()) > nil()                    
0.00/0.15	                                                   
0.00/0.15	  first(cons(; Y); s()) > cons(; Y)                
0.00/0.15	                                                   
0.00/0.15	
0.00/0.15	Hurray, we answered YES(?,O(1))
0.00/0.15	EOF