YES(?,O(n^1)) 2.26/1.42 YES(?,O(n^1)) 2.26/1.42 2.26/1.42 We are left with following problem, upon which TcT provides the 2.26/1.42 certificate YES(?,O(n^1)). 2.26/1.42 2.26/1.42 Strict Trs: { f(f(a())) -> f(g()) } 2.26/1.42 Obligation: 2.26/1.42 derivational complexity 2.26/1.42 Answer: 2.26/1.42 YES(?,O(n^1)) 2.26/1.42 2.26/1.42 TcT has computed the following matrix interpretation satisfying 2.26/1.42 not(EDA) and not(IDA(1)). 2.26/1.42 2.26/1.42 [1 0 0 1] [0] 2.26/1.42 [f](x1) = [0 0 0 0] x1 + [0] 2.26/1.42 [0 0 0 0] [0] 2.26/1.42 [0 0 0 0] [1] 2.26/1.42 2.26/1.42 [0] 2.26/1.42 [a] = [0] 2.26/1.42 [0] 2.26/1.42 [0] 2.26/1.42 2.26/1.42 [0] 2.26/1.42 [g] = [0] 2.26/1.42 [0] 2.26/1.42 [0] 2.26/1.42 2.26/1.42 The order satisfies the following ordering constraints: 2.26/1.42 2.26/1.42 [f(f(a()))] = [1] 2.26/1.42 [0] 2.26/1.42 [0] 2.26/1.42 [1] 2.26/1.42 > [0] 2.26/1.42 [0] 2.26/1.42 [0] 2.26/1.42 [1] 2.26/1.42 = [f(g())] 2.26/1.42 2.26/1.42 2.26/1.42 Hurray, we answered YES(?,O(n^1)) 2.26/1.43 EOF