YES(?,O(n^1))
0.00/0.42	YES(?,O(n^1))
0.00/0.42	
0.00/0.42	We are left with following problem, upon which TcT provides the
0.00/0.42	certificate YES(?,O(n^1)).
0.00/0.42	
0.00/0.42	Strict Trs:
0.00/0.42	  { not(true()) -> false()
0.00/0.42	  , not(false()) -> true()
0.00/0.42	  , odd(0()) -> false()
0.00/0.42	  , odd(s(x)) -> not(odd(x))
0.00/0.42	  , +(x, 0()) -> x
0.00/0.42	  , +(x, s(y)) -> s(+(x, y))
0.00/0.42	  , +(s(x), y) -> s(+(x, y)) }
0.00/0.42	Obligation:
0.00/0.42	  runtime complexity
0.00/0.42	Answer:
0.00/0.42	  YES(?,O(n^1))
0.00/0.42	
0.00/0.42	The input is overlay and right-linear. Switching to innermost
0.00/0.42	rewriting.
0.00/0.42	
0.00/0.42	We are left with following problem, upon which TcT provides the
0.00/0.42	certificate YES(?,O(n^1)).
0.00/0.42	
0.00/0.42	Strict Trs:
0.00/0.42	  { not(true()) -> false()
0.00/0.42	  , not(false()) -> true()
0.00/0.42	  , odd(0()) -> false()
0.00/0.42	  , odd(s(x)) -> not(odd(x))
0.00/0.42	  , +(x, 0()) -> x
0.00/0.42	  , +(x, s(y)) -> s(+(x, y))
0.00/0.42	  , +(s(x), y) -> s(+(x, y)) }
0.00/0.42	Obligation:
0.00/0.42	  innermost runtime complexity
0.00/0.42	Answer:
0.00/0.42	  YES(?,O(n^1))
0.00/0.42	
0.00/0.42	The input was oriented with the instance of 'Small Polynomial Path
0.00/0.42	Order (PS,1-bounded)' as induced by the safe mapping
0.00/0.42	
0.00/0.42	 safe(not) = {1}, safe(true) = {}, safe(false) = {}, safe(odd) = {},
0.00/0.42	 safe(0) = {}, safe(s) = {1}, safe(+) = {}
0.00/0.42	
0.00/0.42	and precedence
0.00/0.42	
0.00/0.42	 odd > not, + > not, odd ~ + .
0.00/0.42	
0.00/0.42	Following symbols are considered recursive:
0.00/0.42	
0.00/0.42	 {odd, +}
0.00/0.42	
0.00/0.42	The recursion depth is 1.
0.00/0.42	
0.00/0.42	For your convenience, here are the satisfied ordering constraints:
0.00/0.42	
0.00/0.42	   not(; true()) > false()       
0.00/0.42	                                 
0.00/0.42	  not(; false()) > true()        
0.00/0.42	                                 
0.00/0.42	       odd(0();) > false()       
0.00/0.42	                                 
0.00/0.42	    odd(s(; x);) > not(; odd(x;))
0.00/0.42	                                 
0.00/0.42	     +(x,  0();) > x             
0.00/0.42	                                 
0.00/0.42	  +(x,  s(; y);) > s(; +(x,  y;))
0.00/0.42	                                 
0.00/0.42	  +(s(; x),  y;) > s(; +(x,  y;))
0.00/0.42	                                 
0.00/0.42	
0.00/0.42	Hurray, we answered YES(?,O(n^1))
0.00/0.42	EOF