YES(?,O(n^1)) 0.00/0.25 YES(?,O(n^1)) 0.00/0.25 0.00/0.25 We are left with following problem, upon which TcT provides the 0.00/0.25 certificate YES(?,O(n^1)). 0.00/0.25 0.00/0.25 Strict Trs: 0.00/0.25 { +(0(), y) -> y 0.00/0.25 , +(s(x), y) -> s(+(x, y)) 0.00/0.25 , -(x, 0()) -> x 0.00/0.25 , -(0(), y) -> 0() 0.00/0.25 , -(s(x), s(y)) -> -(x, y) } 0.00/0.25 Obligation: 0.00/0.25 innermost runtime complexity 0.00/0.25 Answer: 0.00/0.25 YES(?,O(n^1)) 0.00/0.25 0.00/0.25 The input was oriented with the instance of 'Small Polynomial Path 0.00/0.25 Order (PS,1-bounded)' as induced by the safe mapping 0.00/0.25 0.00/0.25 safe(+) = {}, safe(0) = {}, safe(s) = {1}, safe(-) = {2} 0.00/0.25 0.00/0.25 and precedence 0.00/0.25 0.00/0.25 empty . 0.00/0.25 0.00/0.25 Following symbols are considered recursive: 0.00/0.25 0.00/0.25 {+, -} 0.00/0.25 0.00/0.25 The recursion depth is 1. 0.00/0.25 0.00/0.25 For your convenience, here are the satisfied ordering constraints: 0.00/0.25 0.00/0.25 +(0(), y;) > y 0.00/0.25 0.00/0.25 +(s(; x), y;) > s(; +(x, y;)) 0.00/0.25 0.00/0.25 -(x; 0()) > x 0.00/0.25 0.00/0.25 -(0(); y) > 0() 0.00/0.25 0.00/0.25 -(s(; x); s(; y)) > -(x; y) 0.00/0.25 0.00/0.25 0.00/0.25 Hurray, we answered YES(?,O(n^1)) 0.00/0.25 EOF