YES(?,O(n^1)) 34.12/19.92 YES(?,O(n^1)) 34.12/19.92 34.12/19.92 We are left with following problem, upon which TcT provides the 34.12/19.92 certificate YES(?,O(n^1)). 34.12/19.92 34.12/19.92 Strict Trs: 34.12/19.92 { f(X) -> n__f(X) 34.12/19.92 , f(0()) -> cons(0(), n__f(s(0()))) 34.12/19.92 , f(s(0())) -> f(p(s(0()))) 34.12/19.92 , p(s(0())) -> 0() 34.12/19.92 , activate(X) -> X 34.12/19.92 , activate(n__f(X)) -> f(X) } 34.12/19.92 Obligation: 34.12/19.92 derivational complexity 34.12/19.92 Answer: 34.12/19.92 YES(?,O(n^1)) 34.12/19.92 34.12/19.92 The problem is match-bounded by 2. The enriched problem is 34.12/19.92 compatible with the following automaton. 34.12/19.92 { f_0(1) -> 1 34.12/19.92 , f_1(1) -> 1 34.12/19.92 , f_1(6) -> 1 34.12/19.92 , 0_0() -> 1 34.12/19.92 , 0_1() -> 1 34.12/19.92 , 0_1() -> 2 34.12/19.92 , 0_1() -> 5 34.12/19.92 , 0_2() -> 6 34.12/19.92 , cons_0(1, 1) -> 1 34.12/19.92 , cons_1(2, 3) -> 1 34.12/19.92 , cons_2(6, 7) -> 1 34.12/19.92 , n__f_0(1) -> 1 34.12/19.92 , n__f_1(1) -> 1 34.12/19.92 , n__f_1(4) -> 3 34.12/19.92 , n__f_2(1) -> 1 34.12/19.92 , n__f_2(6) -> 1 34.12/19.92 , n__f_2(8) -> 7 34.12/19.92 , s_0(1) -> 1 34.12/19.92 , s_1(5) -> 4 34.12/19.92 , s_2(6) -> 8 34.12/19.92 , p_0(1) -> 1 34.12/19.92 , p_1(4) -> 6 34.12/19.92 , activate_0(1) -> 1 } 34.12/19.92 34.12/19.92 Hurray, we answered YES(?,O(n^1)) 34.12/19.93 EOF