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 { eq0(S(x'), S(x)) -> eq0(x', x) 0.00/0.17 , eq0(S(x), 0()) -> 0() 0.00/0.17 , eq0(0(), S(x)) -> 0() 0.00/0.17 , eq0(0(), 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(eq0) = {1}, safe(S) = {1}, safe(0) = {} 0.00/0.17 0.00/0.17 and precedence 0.00/0.17 0.00/0.17 empty . 0.00/0.17 0.00/0.17 Following symbols are considered recursive: 0.00/0.17 0.00/0.17 {eq0} 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 eq0(S(; x); S(; x')) > eq0(x; x') 0.00/0.17 0.00/0.17 eq0(0(); S(; x)) > 0() 0.00/0.17 0.00/0.17 eq0(S(; x); 0()) > 0() 0.00/0.17 0.00/0.17 eq0(0(); 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