YES(?,O(n^1)) 9.94/5.41 YES(?,O(n^1)) 9.94/5.41 9.94/5.41 We are left with following problem, upon which TcT provides the 9.94/5.41 certificate YES(?,O(n^1)). 9.94/5.41 9.94/5.41 Strict Trs: 9.94/5.41 { f(x, f(f(a(), a()), a())) -> f(f(a(), f(a(), a())), x) } 9.94/5.41 Obligation: 9.94/5.41 derivational complexity 9.94/5.41 Answer: 9.94/5.41 YES(?,O(n^1)) 9.94/5.41 9.94/5.41 TcT has computed the following matrix interpretation satisfying 9.94/5.41 not(EDA) and not(IDA(1)). 9.94/5.41 9.94/5.41 [1 0 0 1] [1 0 0 0] [0] 9.94/5.41 [f](x1, x2) = [0 0 0 0] x1 + [0 0 0 0] x2 + [0] 9.94/5.41 [0 0 0 0] [0 0 0 0] [0] 9.94/5.41 [0 1 0 0] [0 1 0 0] [0] 9.94/5.41 9.94/5.41 [0] 9.94/5.41 [a] = [1] 9.94/5.41 [0] 9.94/5.41 [0] 9.94/5.41 9.94/5.41 The order satisfies the following ordering constraints: 9.94/5.41 9.94/5.41 [f(x, f(f(a(), a()), a()))] = [1 0 0 1] [2] 9.94/5.41 [0 0 0 0] x + [0] 9.94/5.41 [0 0 0 0] [0] 9.94/5.41 [0 1 0 0] [0] 9.94/5.41 > [1 0 0 0] [1] 9.94/5.41 [0 0 0 0] x + [0] 9.94/5.41 [0 0 0 0] [0] 9.94/5.41 [0 1 0 0] [0] 9.94/5.41 = [f(f(a(), f(a(), a())), x)] 9.94/5.41 9.94/5.41 9.94/5.41 Hurray, we answered YES(?,O(n^1)) 9.94/5.42 EOF