YES(?,O(n^1)) We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { c(c(x)) -> b(c(b(c(x)))) , c(c(b(c(x)))) -> b(a(0(), c(x))) , a(0(), x) -> c(c(x)) } Obligation: innermost runtime complexity Answer: YES(?,O(n^1)) The problem is match-bounded by 2. The enriched problem is compatible with the following automaton. { c_0(2) -> 1 , c_0(4) -> 1 , c_1(2) -> 5 , c_1(4) -> 5 , c_1(5) -> 3 , c_2(2) -> 8 , c_2(4) -> 8 , c_2(7) -> 6 , b_0(2) -> 2 , b_0(4) -> 2 , b_2(6) -> 3 , b_2(8) -> 7 , a_0(2, 2) -> 3 , a_0(2, 4) -> 3 , a_0(4, 2) -> 3 , a_0(4, 4) -> 3 , 0_0() -> 4 } Hurray, we answered YES(?,O(n^1))