YES(?,O(n^1)) 3.73/1.06 YES(?,O(n^1)) 3.73/1.06 3.73/1.06 We are left with following problem, upon which TcT provides the 3.73/1.06 certificate YES(?,O(n^1)). 3.73/1.06 3.73/1.06 Strict Trs: 3.73/1.06 { g(c(x, s(y))) -> g(c(s(x), y)) 3.73/1.06 , f(x) -> x 3.73/1.06 , f(c(s(x), y)) -> f(c(x, s(y))) 3.73/1.06 , f(f(x)) -> f(d(f(x))) } 3.73/1.06 Obligation: 3.73/1.06 innermost runtime complexity 3.73/1.06 Answer: 3.73/1.06 YES(?,O(n^1)) 3.73/1.06 3.73/1.06 Arguments of following rules are not normal-forms: 3.73/1.06 3.73/1.06 { f(f(x)) -> f(d(f(x))) } 3.73/1.06 3.73/1.06 All above mentioned rules can be savely removed. 3.73/1.06 3.73/1.06 We are left with following problem, upon which TcT provides the 3.73/1.06 certificate YES(?,O(n^1)). 3.73/1.06 3.73/1.06 Strict Trs: 3.73/1.06 { g(c(x, s(y))) -> g(c(s(x), y)) 3.73/1.06 , f(x) -> x 3.73/1.06 , f(c(s(x), y)) -> f(c(x, s(y))) } 3.73/1.06 Obligation: 3.73/1.06 innermost runtime complexity 3.73/1.06 Answer: 3.73/1.06 YES(?,O(n^1)) 3.73/1.06 3.73/1.06 The problem is match-bounded by 1. The enriched problem is 3.73/1.06 compatible with the following automaton. 3.73/1.06 { g_0(2) -> 1 3.73/1.06 , g_1(3) -> 1 3.73/1.06 , c_0(2, 2) -> 1 3.73/1.06 , c_0(2, 2) -> 2 3.73/1.06 , c_1(2, 4) -> 1 3.73/1.06 , c_1(2, 4) -> 5 3.73/1.06 , c_1(4, 2) -> 3 3.73/1.06 , s_0(2) -> 1 3.73/1.06 , s_0(2) -> 2 3.73/1.06 , s_1(2) -> 4 3.73/1.06 , s_1(4) -> 4 3.73/1.06 , f_0(2) -> 1 3.73/1.06 , f_1(5) -> 1 } 3.73/1.06 3.73/1.06 Hurray, we answered YES(?,O(n^1)) 3.73/1.06 EOF