YES(?,O(n^1))
0.00/0.34	YES(?,O(n^1))
0.00/0.34	
0.00/0.34	We are left with following problem, upon which TcT provides the
0.00/0.34	certificate YES(?,O(n^1)).
0.00/0.34	
0.00/0.34	Strict Trs:
0.00/0.34	  { f(X) -> n__f(X)
0.00/0.34	  , f(f(a())) -> c(n__f(n__g(n__f(n__a()))))
0.00/0.34	  , a() -> n__a()
0.00/0.34	  , g(X) -> n__g(X)
0.00/0.34	  , activate(X) -> X
0.00/0.34	  , activate(n__f(X)) -> f(activate(X))
0.00/0.34	  , activate(n__g(X)) -> g(activate(X))
0.00/0.34	  , activate(n__a()) -> a() }
0.00/0.34	Obligation:
0.00/0.34	  innermost runtime complexity
0.00/0.34	Answer:
0.00/0.34	  YES(?,O(n^1))
0.00/0.34	
0.00/0.34	Arguments of following rules are not normal-forms:
0.00/0.34	
0.00/0.34	{ f(f(a())) -> c(n__f(n__g(n__f(n__a())))) }
0.00/0.34	
0.00/0.34	All above mentioned rules can be savely removed.
0.00/0.34	
0.00/0.34	We are left with following problem, upon which TcT provides the
0.00/0.34	certificate YES(?,O(n^1)).
0.00/0.34	
0.00/0.34	Strict Trs:
0.00/0.34	  { f(X) -> n__f(X)
0.00/0.34	  , a() -> n__a()
0.00/0.34	  , g(X) -> n__g(X)
0.00/0.34	  , activate(X) -> X
0.00/0.34	  , activate(n__f(X)) -> f(activate(X))
0.00/0.34	  , activate(n__g(X)) -> g(activate(X))
0.00/0.34	  , activate(n__a()) -> a() }
0.00/0.34	Obligation:
0.00/0.34	  innermost runtime complexity
0.00/0.34	Answer:
0.00/0.34	  YES(?,O(n^1))
0.00/0.34	
0.00/0.34	The input was oriented with the instance of 'Small Polynomial Path
0.00/0.34	Order (PS,1-bounded)' as induced by the safe mapping
0.00/0.34	
0.00/0.34	 safe(f) = {1}, safe(a) = {}, safe(n__f) = {1}, safe(n__g) = {1},
0.00/0.34	 safe(n__a) = {}, safe(g) = {1}, safe(activate) = {}
0.00/0.34	
0.00/0.34	and precedence
0.00/0.34	
0.00/0.34	 activate > f, activate > a, activate > g, f ~ a, f ~ g, a ~ g .
0.00/0.34	
0.00/0.34	Following symbols are considered recursive:
0.00/0.34	
0.00/0.34	 {activate}
0.00/0.34	
0.00/0.34	The recursion depth is 1.
0.00/0.34	
0.00/0.34	For your convenience, here are the satisfied ordering constraints:
0.00/0.34	
0.00/0.34	                f(; X) > n__f(; X)        
0.00/0.34	                                          
0.00/0.34	                   a() > n__a()           
0.00/0.34	                                          
0.00/0.34	                g(; X) > n__g(; X)        
0.00/0.34	                                          
0.00/0.34	          activate(X;) > X                
0.00/0.34	                                          
0.00/0.34	  activate(n__f(; X);) > f(; activate(X;))
0.00/0.34	                                          
0.00/0.34	  activate(n__g(; X);) > g(; activate(X;))
0.00/0.34	                                          
0.00/0.34	     activate(n__a();) > a()              
0.00/0.34	                                          
0.00/0.34	
0.00/0.34	Hurray, we answered YES(?,O(n^1))
0.00/0.34	EOF