YES(?,O(n^1)) 0.00/0.39 YES(?,O(n^1)) 0.00/0.39 0.00/0.39 We are left with following problem, upon which TcT provides the 0.00/0.39 certificate YES(?,O(n^1)). 0.00/0.39 0.00/0.39 Strict Trs: 0.00/0.39 { dbl(S(0()), S(0())) -> S(S(S(S(0())))) 0.00/0.39 , dbl(0(), y) -> y 0.00/0.39 , unsafe(S(x)) -> dbl(unsafe(x), 0()) 0.00/0.39 , unsafe(0()) -> 0() } 0.00/0.39 Obligation: 0.00/0.39 innermost runtime complexity 0.00/0.39 Answer: 0.00/0.39 YES(?,O(n^1)) 0.00/0.39 0.00/0.39 The input was oriented with the instance of 'Small Polynomial Path 0.00/0.39 Order (PS,1-bounded)' as induced by the safe mapping 0.00/0.39 0.00/0.39 safe(dbl) = {1, 2}, safe(S) = {1}, safe(0) = {}, safe(unsafe) = {} 0.00/0.39 0.00/0.39 and precedence 0.00/0.39 0.00/0.39 unsafe > dbl . 0.00/0.39 0.00/0.39 Following symbols are considered recursive: 0.00/0.39 0.00/0.39 {unsafe} 0.00/0.39 0.00/0.39 The recursion depth is 1. 0.00/0.39 0.00/0.39 For your convenience, here are the satisfied ordering constraints: 0.00/0.39 0.00/0.39 dbl(; S(; 0()), S(; 0())) > S(; S(; S(; S(; 0())))) 0.00/0.39 0.00/0.39 dbl(; 0(), y) > y 0.00/0.39 0.00/0.39 unsafe(S(; x);) > dbl(; unsafe(x;), 0()) 0.00/0.39 0.00/0.39 unsafe(0();) > 0() 0.00/0.39 0.00/0.39 0.00/0.39 Hurray, we answered YES(?,O(n^1)) 0.00/0.39 EOF