YES(?,O(n^1)) 0.00/0.14 YES(?,O(n^1)) 0.00/0.14 0.00/0.14 We are left with following problem, upon which TcT provides the 0.00/0.14 certificate YES(?,O(n^1)). 0.00/0.14 0.00/0.14 Strict Trs: 0.00/0.14 { list(Cons(x, xs)) -> list(xs) 0.00/0.14 , list(Nil()) -> True() 0.00/0.14 , list(Nil()) -> isEmpty[Match](Nil()) 0.00/0.14 , notEmpty(Cons(x, xs)) -> True() 0.00/0.14 , notEmpty(Nil()) -> False() 0.00/0.14 , goal(x) -> list(x) } 0.00/0.14 Obligation: 0.00/0.14 innermost runtime complexity 0.00/0.14 Answer: 0.00/0.14 YES(?,O(n^1)) 0.00/0.14 0.00/0.14 The input was oriented with the instance of 'Small Polynomial Path 0.00/0.14 Order (PS,1-bounded)' as induced by the safe mapping 0.00/0.14 0.00/0.14 safe(list) = {}, safe(Cons) = {1, 2}, safe(Nil) = {}, 0.00/0.14 safe(True) = {}, safe(isEmpty[Match]) = {1}, safe(notEmpty) = {}, 0.00/0.14 safe(False) = {}, safe(goal) = {} 0.00/0.14 0.00/0.14 and precedence 0.00/0.14 0.00/0.14 notEmpty > list, goal > list, notEmpty ~ goal . 0.00/0.14 0.00/0.14 Following symbols are considered recursive: 0.00/0.14 0.00/0.14 {list} 0.00/0.14 0.00/0.14 The recursion depth is 1. 0.00/0.14 0.00/0.14 For your convenience, here are the satisfied ordering constraints: 0.00/0.14 0.00/0.14 list(Cons(; x, xs);) > list(xs;) 0.00/0.14 0.00/0.14 list(Nil();) > True() 0.00/0.14 0.00/0.14 list(Nil();) > isEmpty[Match](; Nil()) 0.00/0.14 0.00/0.14 notEmpty(Cons(; x, xs);) > True() 0.00/0.14 0.00/0.14 notEmpty(Nil();) > False() 0.00/0.14 0.00/0.14 goal(x;) > list(x;) 0.00/0.14 0.00/0.14 0.00/0.14 Hurray, we answered YES(?,O(n^1)) 0.00/0.14 EOF