We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { +(+(x, y), z) -> +(x, +(y, z)) , +(f(x), +(f(y), z)) -> +(f(+(x, y)), z) , +(f(x), f(y)) -> f(+(x, y)) } Obligation: innermost runtime complexity Answer: YES(?,O(n^1)) The problem is match-bounded by 1. The enriched problem is compatible with the following automaton. { +_0(2, 2) -> 1 , +_1(2, 2) -> 3 , f_0(2) -> 2 , f_1(3) -> 1 , f_1(3) -> 3 } Hurray, we answered YES(?,O(n^1))