YES(?,O(n^1)) We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { a(b(x)) -> a(c(b(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. { a_0(2) -> 1 , a_0(3) -> 1 , a_1(4) -> 1 , b_0(2) -> 2 , b_0(3) -> 2 , b_1(2) -> 5 , b_1(3) -> 5 , c_0(2) -> 3 , c_0(3) -> 3 , c_1(5) -> 4 } Hurray, we answered YES(?,O(n^1))