We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { minus(minus(x)) -> x , minus(h(x)) -> h(minus(x)) , minus(f(x, y)) -> f(minus(y), minus(x)) } 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. { minus_0(2) -> 1 , minus_1(2) -> 3 , h_0(2) -> 2 , h_1(3) -> 1 , h_1(3) -> 3 , f_0(2, 2) -> 2 , f_1(3, 3) -> 1 , f_1(3, 3) -> 3 } Hurray, we answered YES(?,O(n^1))