YES(?,O(n^1)) 0.00/0.61 YES(?,O(n^1)) 0.00/0.61 0.00/0.61 We are left with following problem, upon which TcT provides the 0.00/0.61 certificate YES(?,O(n^1)). 0.00/0.61 0.00/0.61 Strict Trs: 0.00/0.61 { g(x, h(y, z)) -> h(g(x, y), z) 0.00/0.61 , g(f(x, y), z) -> f(x, g(y, z)) 0.00/0.61 , g(h(x, y), z) -> g(x, f(y, z)) } 0.00/0.61 Obligation: 0.00/0.61 runtime complexity 0.00/0.61 Answer: 0.00/0.61 YES(?,O(n^1)) 0.00/0.61 0.00/0.61 The input is overlay and right-linear. Switching to innermost 0.00/0.61 rewriting. 0.00/0.61 0.00/0.61 We are left with following problem, upon which TcT provides the 0.00/0.61 certificate YES(?,O(n^1)). 0.00/0.61 0.00/0.61 Strict Trs: 0.00/0.61 { g(x, h(y, z)) -> h(g(x, y), z) 0.00/0.61 , g(f(x, y), z) -> f(x, g(y, z)) 0.00/0.61 , g(h(x, y), z) -> g(x, f(y, z)) } 0.00/0.61 Obligation: 0.00/0.61 innermost runtime complexity 0.00/0.61 Answer: 0.00/0.61 YES(?,O(n^1)) 0.00/0.61 0.00/0.61 The problem is match-bounded by 1. The enriched problem is 0.00/0.61 compatible with the following automaton. 0.00/0.61 { g_0(2, 2) -> 1 0.00/0.61 , g_1(2, 2) -> 3 0.00/0.61 , g_1(2, 4) -> 1 0.00/0.61 , g_1(2, 4) -> 3 0.00/0.61 , f_0(2, 2) -> 2 0.00/0.61 , f_1(2, 2) -> 4 0.00/0.61 , f_1(2, 3) -> 1 0.00/0.61 , f_1(2, 3) -> 3 0.00/0.61 , f_1(2, 4) -> 4 0.00/0.61 , h_0(2, 2) -> 2 0.00/0.61 , h_1(3, 2) -> 1 0.00/0.61 , h_1(3, 2) -> 3 } 0.00/0.61 0.00/0.61 Hurray, we answered YES(?,O(n^1)) 0.00/0.61 EOF