YES(?,O(n^1)) 38.44/18.35 YES(?,O(n^1)) 38.44/18.35 38.44/18.35 We are left with following problem, upon which TcT provides the 38.44/18.35 certificate YES(?,O(n^1)). 38.44/18.35 38.44/18.35 Strict Trs: 38.44/18.35 { f(X) -> n__f(X) 38.44/18.35 , f(0()) -> cons(0(), n__f(s(0()))) 38.44/18.35 , f(s(0())) -> f(p(s(0()))) 38.44/18.35 , p(s(X)) -> X 38.44/18.35 , activate(X) -> X 38.44/18.35 , activate(n__f(X)) -> f(X) } 38.44/18.35 Obligation: 38.44/18.35 derivational complexity 38.44/18.35 Answer: 38.44/18.35 YES(?,O(n^1)) 38.44/18.35 38.44/18.35 The problem is match-bounded by 2. The enriched problem is 38.44/18.35 compatible with the following automaton. 38.44/18.35 { f_0(1) -> 1 38.44/18.35 , f_1(1) -> 1 38.44/18.35 , f_1(6) -> 1 38.44/18.35 , 0_0() -> 1 38.44/18.35 , 0_1() -> 2 38.44/18.35 , 0_1() -> 5 38.44/18.35 , 0_1() -> 6 38.44/18.35 , 0_2() -> 7 38.44/18.35 , 0_2() -> 10 38.44/18.35 , cons_0(1, 1) -> 1 38.44/18.35 , cons_1(2, 3) -> 1 38.44/18.35 , cons_2(7, 8) -> 1 38.44/18.35 , n__f_0(1) -> 1 38.44/18.35 , n__f_1(1) -> 1 38.44/18.35 , n__f_1(4) -> 3 38.44/18.35 , n__f_2(1) -> 1 38.44/18.35 , n__f_2(6) -> 1 38.44/18.35 , n__f_2(9) -> 8 38.44/18.35 , s_0(1) -> 1 38.44/18.35 , s_1(5) -> 4 38.44/18.35 , s_2(10) -> 9 38.44/18.35 , p_0(1) -> 1 38.44/18.35 , p_1(4) -> 6 38.44/18.35 , activate_0(1) -> 1 } 38.44/18.35 38.44/18.35 Hurray, we answered YES(?,O(n^1)) 38.44/18.36 EOF