YES(?,O(n^1))
0.00/0.46	YES(?,O(n^1))
0.00/0.46	
0.00/0.46	We are left with following problem, upon which TcT provides the
0.00/0.46	certificate YES(?,O(n^1)).
0.00/0.46	
0.00/0.46	Strict Trs:
0.00/0.46	  { div2(S(S(x))) -> +(S(0()), div2(x))
0.00/0.46	  , div2(S(0())) -> 0()
0.00/0.46	  , div2(0()) -> 0() }
0.00/0.46	Weak Trs:
0.00/0.46	  { +(x, S(0())) -> S(x)
0.00/0.46	  , +(S(0()), y) -> S(y) }
0.00/0.46	Obligation:
0.00/0.46	  innermost runtime complexity
0.00/0.46	Answer:
0.00/0.46	  YES(?,O(n^1))
0.00/0.46	
0.00/0.46	The input was oriented with the instance of 'Small Polynomial Path
0.00/0.46	Order (PS,1-bounded)' as induced by the safe mapping
0.00/0.46	
0.00/0.46	 safe(div2) = {}, safe(+) = {1, 2}, safe(S) = {1}, safe(0) = {}
0.00/0.46	
0.00/0.46	and precedence
0.00/0.46	
0.00/0.46	 div2 > + .
0.00/0.46	
0.00/0.46	Following symbols are considered recursive:
0.00/0.46	
0.00/0.46	 {div2}
0.00/0.46	
0.00/0.46	The recursion depth is 1.
0.00/0.46	
0.00/0.46	For your convenience, here are the satisfied ordering constraints:
0.00/0.46	
0.00/0.46	  div2(S(; S(; x));) > +(; S(; 0()),  div2(x;))
0.00/0.46	                                               
0.00/0.46	     div2(S(; 0());) > 0()                     
0.00/0.46	                                               
0.00/0.46	          div2(0();) > 0()                     
0.00/0.46	                                               
0.00/0.46	   +(; x,  S(; 0())) > S(; x)                  
0.00/0.46	                                               
0.00/0.46	   +(; S(; 0()),  y) > S(; y)                  
0.00/0.46	                                               
0.00/0.46	
0.00/0.46	Hurray, we answered YES(?,O(n^1))
0.00/0.46	EOF