YES(?,O(n^1)) 4.85/2.88 YES(?,O(n^1)) 4.85/2.88 4.85/2.88 We are left with following problem, upon which TcT provides the 4.85/2.88 certificate YES(?,O(n^1)). 4.85/2.88 4.85/2.88 Strict Trs: 4.85/2.88 { g(0()) -> 0() 4.85/2.88 , g(s(x)) -> f(g(x)) 4.85/2.88 , f(0()) -> 0() } 4.85/2.88 Obligation: 4.85/2.88 derivational complexity 4.85/2.88 Answer: 4.85/2.88 YES(?,O(n^1)) 4.85/2.88 4.85/2.88 TcT has computed the following matrix interpretation satisfying 4.85/2.88 not(EDA) and not(IDA(1)). 4.85/2.88 4.85/2.88 [1 1 0 0] [1] 4.85/2.88 [g](x1) = [0 0 0 0] x1 + [0] 4.85/2.88 [0 0 0 0] [0] 4.85/2.88 [0 0 0 0] [0] 4.85/2.88 4.85/2.88 [0] 4.85/2.88 [0] = [0] 4.85/2.88 [0] 4.85/2.88 [0] 4.85/2.88 4.85/2.88 [1 1 0 0] [1] 4.85/2.88 [s](x1) = [0 0 0 0] x1 + [1] 4.85/2.88 [0 0 0 0] [0] 4.85/2.88 [0 0 0 0] [0] 4.85/2.88 4.85/2.88 [1 0 0 0] [1] 4.85/2.88 [f](x1) = [0 0 0 0] x1 + [0] 4.85/2.88 [0 0 0 0] [0] 4.85/2.88 [0 0 0 0] [0] 4.85/2.88 4.85/2.88 The order satisfies the following ordering constraints: 4.85/2.88 4.85/2.88 [g(0())] = [1] 4.85/2.88 [0] 4.85/2.88 [0] 4.85/2.88 [0] 4.85/2.88 > [0] 4.85/2.88 [0] 4.85/2.88 [0] 4.85/2.88 [0] 4.85/2.88 = [0()] 4.85/2.88 4.85/2.88 [g(s(x))] = [1 1 0 0] [3] 4.85/2.88 [0 0 0 0] x + [0] 4.85/2.88 [0 0 0 0] [0] 4.85/2.88 [0 0 0 0] [0] 4.85/2.88 > [1 1 0 0] [2] 4.85/2.88 [0 0 0 0] x + [0] 4.85/2.88 [0 0 0 0] [0] 4.85/2.88 [0 0 0 0] [0] 4.85/2.88 = [f(g(x))] 4.85/2.88 4.85/2.88 [f(0())] = [1] 4.85/2.88 [0] 4.85/2.88 [0] 4.85/2.88 [0] 4.85/2.88 > [0] 4.85/2.88 [0] 4.85/2.88 [0] 4.85/2.88 [0] 4.85/2.88 = [0()] 4.85/2.88 4.85/2.88 4.85/2.88 Hurray, we answered YES(?,O(n^1)) 4.85/2.89 EOF