YES(?,O(n^1)) 0.00/0.86 YES(?,O(n^1)) 0.00/0.86 0.00/0.86 We are left with following problem, upon which TcT provides the 0.00/0.86 certificate YES(?,O(n^1)). 0.00/0.86 0.00/0.86 Strict Trs: 0.00/0.86 { not(true()) -> false() 0.00/0.86 , not(false()) -> true() 0.00/0.86 , evenodd(x, 0()) -> not(evenodd(x, s(0()))) 0.00/0.86 , evenodd(0(), s(0())) -> false() 0.00/0.86 , evenodd(s(x), s(0())) -> evenodd(x, 0()) } 0.00/0.86 Obligation: 0.00/0.86 innermost runtime complexity 0.00/0.86 Answer: 0.00/0.86 YES(?,O(n^1)) 0.00/0.86 0.00/0.86 The problem is match-bounded by 3. The enriched problem is 0.00/0.86 compatible with the following automaton. 0.00/0.86 { not_0(2) -> 1 0.00/0.86 , not_1(3) -> 1 0.00/0.86 , not_2(6) -> 1 0.00/0.86 , not_2(6) -> 3 0.00/0.86 , not_2(6) -> 6 0.00/0.86 , true_0() -> 2 0.00/0.86 , true_1() -> 1 0.00/0.86 , true_2() -> 1 0.00/0.86 , true_2() -> 3 0.00/0.86 , true_2() -> 6 0.00/0.86 , true_3() -> 1 0.00/0.86 , true_3() -> 3 0.00/0.86 , true_3() -> 6 0.00/0.86 , false_0() -> 2 0.00/0.86 , false_1() -> 1 0.00/0.86 , false_1() -> 3 0.00/0.86 , false_1() -> 6 0.00/0.86 , false_2() -> 1 0.00/0.86 , false_3() -> 1 0.00/0.86 , false_3() -> 3 0.00/0.86 , false_3() -> 6 0.00/0.86 , evenodd_0(2, 2) -> 1 0.00/0.86 , evenodd_1(2, 4) -> 3 0.00/0.86 , evenodd_1(2, 5) -> 1 0.00/0.86 , evenodd_1(2, 5) -> 3 0.00/0.86 , evenodd_1(2, 5) -> 6 0.00/0.86 , evenodd_2(2, 7) -> 6 0.00/0.86 , 0_0() -> 2 0.00/0.86 , 0_1() -> 5 0.00/0.86 , 0_2() -> 8 0.00/0.86 , s_0(2) -> 2 0.00/0.86 , s_1(5) -> 4 0.00/0.86 , s_2(8) -> 7 } 0.00/0.87 0.00/0.87 Hurray, we answered YES(?,O(n^1)) 0.00/0.87 EOF