YES(?,O(n^1)) 0.00/0.99 YES(?,O(n^1)) 0.00/0.99 0.00/0.99 We are left with following problem, upon which TcT provides the 0.00/0.99 certificate YES(?,O(n^1)). 0.00/0.99 0.00/0.99 Strict Trs: 0.00/0.99 { not(true()) -> false() 0.00/0.99 , not(false()) -> true() 0.00/0.99 , evenodd(x, 0()) -> not(evenodd(x, s(0()))) 0.00/0.99 , evenodd(0(), s(0())) -> false() 0.00/0.99 , evenodd(s(x), s(0())) -> evenodd(x, 0()) } 0.00/0.99 Obligation: 0.00/0.99 derivational complexity 0.00/0.99 Answer: 0.00/0.99 YES(?,O(n^1)) 0.00/0.99 0.00/0.99 The problem is match-bounded by 3. The enriched problem is 0.00/0.99 compatible with the following automaton. 0.00/0.99 { not_0(1) -> 1 0.00/0.99 , not_1(2) -> 1 0.00/0.99 , not_2(5) -> 1 0.00/0.99 , not_2(5) -> 2 0.00/0.99 , not_2(5) -> 5 0.00/0.99 , true_0() -> 1 0.00/0.99 , true_1() -> 1 0.00/0.99 , true_2() -> 1 0.00/0.99 , true_2() -> 2 0.00/0.99 , true_2() -> 5 0.00/0.99 , true_3() -> 1 0.00/0.99 , true_3() -> 2 0.00/0.99 , true_3() -> 5 0.00/0.99 , false_0() -> 1 0.00/0.99 , false_1() -> 1 0.00/0.99 , false_1() -> 2 0.00/0.99 , false_1() -> 5 0.00/0.99 , false_2() -> 1 0.00/0.99 , false_3() -> 1 0.00/0.99 , false_3() -> 2 0.00/0.99 , false_3() -> 5 0.00/0.99 , evenodd_0(1, 1) -> 1 0.00/0.99 , evenodd_1(1, 3) -> 2 0.00/0.99 , evenodd_1(1, 4) -> 1 0.00/0.99 , evenodd_1(1, 4) -> 2 0.00/0.99 , evenodd_1(1, 4) -> 5 0.00/0.99 , evenodd_2(1, 6) -> 5 0.00/0.99 , 0_0() -> 1 0.00/0.99 , 0_1() -> 4 0.00/0.99 , 0_2() -> 7 0.00/0.99 , s_0(1) -> 1 0.00/0.99 , s_1(4) -> 3 0.00/0.99 , s_2(7) -> 6 } 0.00/0.99 0.00/0.99 Hurray, we answered YES(?,O(n^1)) 0.00/0.99 EOF