YES(?,O(n^1)) 0.00/0.17 YES(?,O(n^1)) 0.00/0.17 0.00/0.17 We are left with following problem, upon which TcT provides the 0.00/0.17 certificate YES(?,O(n^1)). 0.00/0.17 0.00/0.17 Strict Trs: 0.00/0.17 { g(s(x)) -> f(x) 0.00/0.17 , g(0()) -> 0() 0.00/0.17 , f(s(x)) -> s(s(g(x))) 0.00/0.17 , f(0()) -> s(0()) } 0.00/0.17 Obligation: 0.00/0.17 innermost runtime complexity 0.00/0.17 Answer: 0.00/0.17 YES(?,O(n^1)) 0.00/0.17 0.00/0.17 The input was oriented with the instance of 'Small Polynomial Path 0.00/0.17 Order (PS)' as induced by the safe mapping 0.00/0.17 0.00/0.17 safe(g) = {}, safe(s) = {1}, safe(f) = {}, safe(0) = {} 0.00/0.17 0.00/0.17 and precedence 0.00/0.17 0.00/0.17 g ~ f . 0.00/0.17 0.00/0.17 Following symbols are considered recursive: 0.00/0.17 0.00/0.17 {g, f} 0.00/0.17 0.00/0.17 The recursion depth is 1. 0.00/0.17 0.00/0.17 For your convenience, here are the satisfied ordering constraints: 0.00/0.17 0.00/0.17 g(s(; x);) > f(x;) 0.00/0.17 0.00/0.17 g(0();) > 0() 0.00/0.17 0.00/0.17 f(s(; x);) > s(; s(; g(x;))) 0.00/0.17 0.00/0.17 f(0();) > s(; 0()) 0.00/0.17 0.00/0.17 0.00/0.17 Hurray, we answered YES(?,O(n^1)) 0.00/0.17 EOF