YES(?,O(n^1)) 5.44/3.29 YES(?,O(n^1)) 5.44/3.29 5.44/3.29 We are left with following problem, upon which TcT provides the 5.44/3.29 certificate YES(?,O(n^1)). 5.44/3.29 5.44/3.29 Strict Trs: { a(b(a(x))) -> b(a(b(x))) } 5.44/3.29 Obligation: 5.44/3.29 derivational complexity 5.44/3.29 Answer: 5.44/3.29 YES(?,O(n^1)) 5.44/3.29 5.44/3.29 TcT has computed the following matrix interpretation satisfying 5.44/3.29 not(EDA) and not(IDA(1)). 5.44/3.29 5.44/3.29 [1 0 0 0] [1] 5.44/3.29 [a](x1) = [0 0 0 0] x1 + [0] 5.44/3.29 [0 0 0 0] [0] 5.44/3.29 [0 0 0 0] [0] 5.44/3.29 5.44/3.29 [1 0 0 0] [0] 5.44/3.29 [b](x1) = [0 0 0 0] x1 + [0] 5.44/3.29 [0 0 0 0] [0] 5.44/3.29 [0 0 0 0] [0] 5.44/3.29 5.44/3.29 The order satisfies the following ordering constraints: 5.44/3.29 5.44/3.29 [a(b(a(x)))] = [1 0 0 0] [2] 5.44/3.29 [0 0 0 0] x + [0] 5.44/3.29 [0 0 0 0] [0] 5.44/3.29 [0 0 0 0] [0] 5.44/3.29 > [1 0 0 0] [1] 5.44/3.29 [0 0 0 0] x + [0] 5.44/3.29 [0 0 0 0] [0] 5.44/3.29 [0 0 0 0] [0] 5.44/3.29 = [b(a(b(x)))] 5.44/3.29 5.44/3.29 5.44/3.29 Hurray, we answered YES(?,O(n^1)) 5.44/3.30 EOF