YES(?,O(1)) 0.00/0.06 YES(?,O(1)) 0.00/0.06 0.00/0.06 We are left with following problem, upon which TcT provides the 0.00/0.06 certificate YES(?,O(1)). 0.00/0.06 0.00/0.06 Strict Trs: 0.00/0.06 { f(X) -> n__f(X) 0.00/0.06 , f(f(a())) -> c(n__f(g(f(a())))) 0.00/0.06 , activate(X) -> X 0.00/0.06 , activate(n__f(X)) -> f(X) } 0.00/0.06 Obligation: 0.00/0.06 innermost runtime complexity 0.00/0.06 Answer: 0.00/0.06 YES(?,O(1)) 0.00/0.06 0.00/0.06 Arguments of following rules are not normal-forms: 0.00/0.06 0.00/0.06 { f(f(a())) -> c(n__f(g(f(a())))) } 0.00/0.06 0.00/0.06 All above mentioned rules can be savely removed. 0.00/0.06 0.00/0.06 We are left with following problem, upon which TcT provides the 0.00/0.06 certificate YES(?,O(1)). 0.00/0.06 0.00/0.06 Strict Trs: 0.00/0.06 { f(X) -> n__f(X) 0.00/0.06 , activate(X) -> X 0.00/0.06 , activate(n__f(X)) -> f(X) } 0.00/0.06 Obligation: 0.00/0.06 innermost runtime complexity 0.00/0.06 Answer: 0.00/0.06 YES(?,O(1)) 0.00/0.06 0.00/0.06 The input was oriented with the instance of 'Small Polynomial Path 0.00/0.06 Order (PS,0-bounded)' as induced by the safe mapping 0.00/0.06 0.00/0.06 safe(f) = {}, safe(n__f) = {1}, safe(activate) = {} 0.00/0.06 0.00/0.06 and precedence 0.00/0.06 0.00/0.06 activate > f . 0.00/0.06 0.00/0.06 Following symbols are considered recursive: 0.00/0.06 0.00/0.06 {} 0.00/0.06 0.00/0.06 The recursion depth is 0. 0.00/0.06 0.00/0.06 For your convenience, here are the satisfied ordering constraints: 0.00/0.06 0.00/0.06 f(X;) > n__f(; X) 0.00/0.06 0.00/0.06 activate(X;) > X 0.00/0.06 0.00/0.06 activate(n__f(; X);) > f(X;) 0.00/0.06 0.00/0.06 0.00/0.06 Hurray, we answered YES(?,O(1)) 0.00/0.06 EOF