YES(?,O(n^1)) 35.72/12.76 YES(?,O(n^1)) 35.72/12.76 35.72/12.76 We are left with following problem, upon which TcT provides the 35.72/12.76 certificate YES(?,O(n^1)). 35.72/12.76 35.72/12.76 Strict Trs: 35.72/12.76 { b(x, y) -> c(a(c(y), a(0(), x))) 35.72/12.76 , a(y, x) -> y 35.72/12.76 , a(y, c(b(a(0(), x), 0()))) -> b(a(c(b(0(), y)), x), 0()) } 35.72/12.76 Obligation: 35.72/12.76 runtime complexity 35.72/12.76 Answer: 35.72/12.76 YES(?,O(n^1)) 35.72/12.76 35.72/12.76 The problem is match-bounded by 1. The enriched problem is 35.72/12.76 compatible with the following automaton. 35.72/12.76 { b_0(2, 2) -> 1 35.72/12.76 , b_0(2, 4) -> 1 35.72/12.76 , b_0(4, 2) -> 1 35.72/12.76 , b_0(4, 4) -> 1 35.72/12.76 , c_0(2) -> 2 35.72/12.76 , c_0(2) -> 3 35.72/12.76 , c_0(4) -> 2 35.72/12.76 , c_0(4) -> 3 35.72/12.76 , c_1(2) -> 5 35.72/12.76 , c_1(2) -> 6 35.72/12.76 , c_1(4) -> 5 35.72/12.76 , c_1(4) -> 6 35.72/12.76 , c_1(5) -> 1 35.72/12.76 , a_0(2, 2) -> 3 35.72/12.76 , a_0(2, 4) -> 3 35.72/12.76 , a_0(4, 2) -> 3 35.72/12.76 , a_0(4, 4) -> 3 35.72/12.76 , a_1(6, 7) -> 5 35.72/12.76 , a_1(8, 2) -> 7 35.72/12.76 , a_1(8, 4) -> 7 35.72/12.76 , 0_0() -> 3 35.72/12.76 , 0_0() -> 4 35.72/12.76 , 0_1() -> 7 35.72/12.76 , 0_1() -> 8 } 35.72/12.76 35.72/12.76 Hurray, we answered YES(?,O(n^1)) 35.72/12.79 EOF